"An alternate reality?"
"Precisely. Whatever our lives might have been, if the time continuum was disrupted, our destinies have changed."
The alternate reality was a new reality created on Friday, January 4, 2233 (stardate 2233.04) when a temporal incursion caused by time travel of the Narada, a Romulan mining vessel from the year 2387, disrupted the time continuum of the prime universe.
Accidentally traveling back to that point in time, Nero, the Narada's captain, attacked the USS Kelvin resulting in the deaths of several crew members, including George Kirk and Richard Robau, and the destruction of the Kelvin itself. Spock arrived to the alternate reality in 2258 and was captured by Nero, who used red matter to destroy Vulcan. However, Nero's attacks united the crew of the USS Enterprise, who foiled his attempt to destroy Earth. (Star Trek)
In the prime universe, the Romulan sun threatened to explode in a supernova that could potentially destroy the entire galaxy. Ambassador Spock was able to halt the supernova, via the use of red matter to create an artificial singularity, or black hole, which absorbed the exploding star, but was too late to save the planet Romulus from destruction. The Narada, a Romulan mining ship under the command of Captain Nero, was pulled into the black hole, followed by Spock's ship, the Jellyfish.
As Starfleet had abandoned efforts to evacuate Romulus following the Attack on Mars (PIC: "Remembrance"), Nero placed blame on the Federation for the death toll and sought revenge. He emerged from the black hole in 2233. The USS Kelvin was the first ship that Nero encountered and attacked; Captain Richard Robau promoted his first officer, Lieutenant Commander George Kirk, to captaincy before ordering the evacuation of the ship and agreeing to come aboard the Narada. There, Captain Robau was interrogated regarding the whereabouts of Spock, with whom Robau was unfamiliar and, moments after he informed Nero of the current stardate, he was murdered.
Nero then proceeded to attack the Kelvin. Kirk used the Kelvin's weapons to prevent Nero from destroying the evacuating shuttles departing the ship, ultimately sacrificing himself by ramming the Kelvin into the Narada. Kirk's actions saved some eight hundred lives, including his wife, Winona, and their newborn son, James, but failed to destroy the Narada.
As a major consequence of these events, James Kirk grew up without his father and without the ambitions his father gave him in the prime reality. However, he was persuaded by Christopher Pike to join Starfleet, three years later than he had done in the prime reality.
In the meantime, other events occurred differently. Pavel Chekov was born in 2241, while the Romulans were confirmed as relatives of the Vulcans. Plans for the Constitution-class were pushed back by a decade and the USS Enterprise began construction in 2255 at the Riverside Shipyard in Iowa, with a number of internal, external, and systems design differences to the prime reality version. It was launched three years later, already as the Federation flagship under the command of Captain Pike. Spock was already promoted to commander by this point. Starfleet continued using the simple <Earth calendar year>.<day of the year> format for stardates, and had already begun using gold, blue, and red colors for their uniforms. They also adopted the Kelvin assignment patch as the sole Starfleet insignia. The Vulcan High Command was reinstated as the Vulcan High Council. Some differences in personal relationships also occurred, such as Spock and Nyota Uhura being romantically involved by the time Kirk joins the Enterprise.
Along with the Enterprise, various technological, scientific, and aesthetic aspects of a multitude of cultures, including those of Earth, varied greatly in difference and advancement in comparison with that of the prime reality.
Destruction of Vulcan
In 2258, Nero captured the Jellyfish as it emerged from travel through the black hole. He marooned Spock on Delta Vega, and despite the efforts of the USS Enterprise, he used a portion of the remaining red matter aboard to destroy the planet Vulcan and six billion of its inhabitants, including Amanda Grayson. While marooned on Delta Vega, Spock encountered the alternate James T. Kirk and made him aware of the prime reality and the altered past. He also met Montgomery Scott and gave him the formula for transwarp beaming, which Scott subsequently used to transport Kirk and the young Spock to the Narada, allowing them to prevent a similar fate for Earth by detonating the Jellyfish and its red matter to destroy the Narada.
Afterward, Christopher Pike was promoted to admiral and Kirk and Spock became, respectively, captain and first officer of the Enterprise, which was officially launched on a voyage of exploration, with much of its commanding crew comprised of those who served aboard it in the prime reality during 2267: Kirk, Spock, Scott, Chekov, Leonard McCoy, Hikaru Sulu, and Nyota Uhura. Spock maintained a relationship with Uhura and reconciled with his father, Sarek, following the deaths of his Human mother and most of his own people. Ambassador Spock intended to found a New Vulcan colony on which the ten thousand Vulcan survivors would live and thrive. (Star Trek)
A fearful Federation
By the late 2250s, the head of Starfleet, Admiral Alexander Marcus, had increasingly become concerned about tensions with the Klingons, who, since they were first encountered, had conquered and occupied at least two planets and had fired on Federation ships half a dozen times. Fearing that the Klingons were coming his way, Marcus went in search of potential resources. He found the SS Botany Bay, recovering its seventy-three occupants. He awoke Khan Noonien Singh from cryogenic stasis, and blackmailed him into designing ships and weapons to prepare for the coming war.
The moon of Qo'noS, Praxis, seems to have been already destroyed by 2259. Also, the Treaty of Organia was in existence by February of that year, but on the eve of the founding of Sherman's Planet, there was a dispute about it. A Klingon colony was discovered on the planet Khitomer.
Around the same time, Khan turned on Starfleet, coercing a member of Section 31 into bombing a base of theirs in London. During an emergency meeting in San Francisco, Khan attacked before escaping to an uninhabited area of Qo'noS using the confiscated transwarp beaming formula. During the attack, Admiral Pike was killed, and a vengeful Kirk was given permission to find and terminate Khan. The Enterprise was outfitted with seventy-two advanced long-range torpedoes, with the intent of using these to execute him from orbit.
When the Enterprise arrived at Qo'nos, Kirk opted to apprehend Khan, rather than firing a torpedo on his location. When they found him, Khan killed a Klingon patrol that had intercepted Kirk's away team and submitted to his authority. Aboard the Enterprise, Khan explained his involvement with Marcus, after McCoy and Carol Marcus discovered his crew were contained inside the missiles supplied by the admiral.
Marcus soon arrived on the USS Vengeance, and opted to destroy the Enterprise to cover up the conspiracy. Fortunately, Scott had stowed away on the Vengeance and deactivated its weaponry, giving Kirk and Khan time to space-dive and commandeer the ship. Khan then betrayed Kirk, killing Admiral Marcus, and threatened to resume bombarding the Enterprise unless his people were beamed aboard. The missiles were beamed aboard, but Khan reneged on the deal, forcing Spock to detonate the missiles; however, McCoy had removed the cryo chambers from the missiles before they could be used against the Vengeance.
Both ships were crippled and began descending due to Earth's gravitational pull. Kirk reactivated the Enterprise's warp core before it crashed, but at the cost of fatally poisoning him. When the Vengeance crashed in San Francisco, Spock beamed down to execute Khan in retribution, but McCoy realized Khan's blood could be used to revive Kirk, so Uhura beamed over to stun Khan repeatedly so that Spock could simply knock him out. McCoy then performed a blood transfusion, saving Kirk's life. Khan was placed back in stasis with the rest of his people.
Almost a year later, Captain Kirk presided over a memorial for the lives lost because of Khan and Marcus. The refitted Enterprise was rechristened and sent on the first, unprecedented five-year mission, with the aim of promoting a less militaristic direction for Starfleet. (Star Trek Into Darkness)
Krall's revenge on the Federation
In 2263, the Fibonan Republic charged the United Federation of Planets to act as neutral intermediaries in brokering a truce with the Teenaxi, which was carried out by the USS Enterprise. Unfortunately, the Teenaxi's paranoia completely derailed the negotiations, forcing Kirk to abandon them. As a result, an ancient weapon remained in the starship's archive vault.
Krall, formerly Captain Balthazar M. Edison and commanding officer of the USS Franklin, discovered – from Starfleet logs, accessed through a captured Magellan probe – that this weapon was the second piece of the Abronath. He dispatched Jessica Wolff, now "Kalara", to lure the Enterprise to him.
Upon the arrival of the Enterprise at Altamid, Krall attacked with his Swarm drones. He destroyed the Enterprise, captured most of the crew, and eventually coerced Ensign Syl into relinquishing the second Abronath piece. His weapon complete, Krall departed Altamid with his Swarm to wipe out all life from the nearby Starbase Yorktown, whose multicultural population he saw as the epitome of the Federation's degeneracy.
Krall's Swarm overwhelmed Yorktown's defenses and was on the verge of breaking inside when he was engaged by the USS Franklin, commanded by Captain Kirk. The Franklin used a VHF radio broadcast to disrupt the Swarm's internal communications network and destroyed most of them. Krall managed to enter Yorktown, but the Franklin physically stopped his ship short of his destination.
Having drained many Enterprise crew members before and after the battle, Krall had regained much of his Human physiology and was thus able to disguise himself as a Starfleet officer. This allowed him to make his way unimpeded to the central atmospheric processor on Yorktown, where the Abronath's effects would be disseminated throughout the station. He was intercepted by Kirk, and the two fought while Scott redirected the processor to vent into space; Kirk then ejected both Krall and the Abronath out of Yorktown. Shortly after, Krall was consumed by the Abronath, leaving only the Starfleet insignia from his stolen uniform. Following the defeat of Krall, the new USS Enterprise-A, which had been under construction at Starbase Yorktown, was completed and assigned to the surviving Enterprise senior staff to continue their five-year mission. (Star Trek Beyond)
Yor's time travel crossover
In 2379, Lieutenant commander Yor, a Betelgeusian time soldier, traveled from this reality into the future of the prime universe. As a result, Starfleet in the Prime universe became aware of the alternate reality (as well as, belatedly, the fate of Spock Prime). (DIS: "Terra Firma, Part 1")
The alternate reality runs parallel, existing as a quantum reality, to the prime reality, which is where many of the events seen in the Star Trek universe have occurred. According to Star Trek writers Alex Kurtzman and Roberto Orci, the conceptual invention of the alternate reality allowed the prime reality to continue. 
This intent is also evident in the script of Star Trek.  While not completely audible in the film, before being teased by his classmates, young Spock is asked by the computer in the learning center on Vulcan, "What is the central assumption of quantum cosmology?" to which Spock replies, "Everything that can happen does happen in equal and parallel universes."
As the alternate reality is merely divergent rather than a completely new universe, this means backstory elements pertaining to anything before 2233 hold true for both timelines. Director J.J. Abrams said, "It's actually nice when you're given a box.... when you're given parameters that you have to honor because it gives you limits and then you know that within those boundaries you can be creatively risky." (Memory Alpha:Ask J.J. Abrams/Answers)
On the Star Trek audio commentary, the writers stated some events in the new timeline were meant to give insight as to what happened in the prime reality, such as how Kirk and Spock met following the Kobayashi Maru scandal. Roberto Orci opined that identical events would happen in both timelines because the "rules of quantum mechanics tell us that the universes that exist, they exist because they are the most probable universe [....] The things that happened in the original series didn't just happen because they happened, they happened because it's actually what's most probably going to happen." However, when asked if this meant Spock and Uhura might break up as they were not in a relationship in the prime reality, Orci responded:
- "Their relationship is slightly predestined. On the other hand, our whole point was to give all of our characters free will again. They truly have free will. The universe is not written. The future is not written. And it's not clear what's going to happen. It's going to [be] up to what the characters do. Be it us as the next writers or someone else who has a better idea, may these characters fulfill their destinies according to their own devices and their own free will." 
Roberto Orci, in a post on Ain't It Cool News  as well as in an interview with Star Trek Magazine issue 146 (p. 40), and J.J. Abrams, in an interview with MTV conducted between the two aforementioned statements from Orci, established a reason why technology in the alternate reality appears to be more advanced than it is during the same period in the prime reality. Scans and telemetry of the 24th century Narada, taken by the Kelvin, were brought back to Starfleet by the survivors on the Kelvin's shuttles. Therefore, Starfleet's development and construction plans were slightly altered, making everything potentially more advanced, slightly ahead of schedule.
- "The less than simple fact [is] that time is not linear. Sure, we experience time as a contiguous series of cascading events but perception and reality aren’t always the same thing. Spock's incursion from the Prime Universe created a multidimensional reality shift. The rift in space/time created an entirely new reality in all directions, top to bottom, from the Big Bang to the end of everything. As such this reality was, is and always will be subtly different from the Prime Universe." 
Comics artist Tony Shasteen approved of the alternate reality, commenting, "I can appreciate what is being done with this alternate universe. I feel like it works with what has come before. I know it isn't everyone's cup of tea, but I appreciate it for what it is." 
Name of the timeline
StarTrek.com originally differentiated the new versions of the characters introduced in Star Trek with the initials "AR", and some pages used "09" as a disambiguation in the web address. Within their online database, the timeline is interchangeably described as the Nero-created "alternate reality",  "alternate dimension",  "alternate timeline",  and "alternate universe". . After 2016, some entries in the database were updated to switch to the disambiguation "Kelvin", but retained the interchangeable "alternate" text in the entries themselves. 
In an interview, actress Alice Eve called it the "split universe".  Simon Pegg joked, "I had this idea. I think that we might all be the mirror universe crew." Perhaps in the third movie, we'll see that "something's going to go to shit, we're all going to turn bad, Spock's going to grow a beard, and we're going to meet ourselves. That could happen." 
IDW Publishing calls the alternate reality the "new timeline" or the "altered" timeline/continuity. The board game Star Trek: Expeditions calls it the "new universe". As some former Star Trek production staffers, like Doug Drexler, did, author of Star Trek novels Christopher L. Bennett has referred to it as the "Abramsverse",  and noted the slang term prefix "Nu", which gave him "the impression that it was the label favored by people who wanted to dismiss the Abrams continuity or make it sound ridiculous." 
Al Rivera, head developer of Star Trek Online, announced that CBS had endowed the timeline with the non-canon "Kelvin Timeline" moniker.  Michael and Denise Okuda settled on the name after much deliberation for the fourth edition of the Star Trek Encyclopedia of 2016.  In June of 2016 CBS Consumer Products, the official guardian of the Star Trek franchise, confirmed that Okuda was actually tasked with creating a new moniker to commercial/promotional ends, and that it, at least where the franchise is concerned, has become the "official" one.  The first publication to include reference to this term was The Star Trek Book from June 2016, before the Encyclopedia was released. After several subsequent print publications such as the 2017 The Art of Star Trek: The Kelvin Timeline reference book, the franchise moniker was for the first time used for a home video format in June 2019 with the release of the Star Trek Trilogy: The Kelvin Timeline Blu-ray Disc set of the three alternate reality films on the occasion of the 10th anniversary of the alternate reality.
For internal consistency reasons, especially where the in-universe articles are concerned, Memory Alpha adheres to the "alternate reality" denominator as it is of all the alternatives the only one actually used on screen, when it was uttered by Uhura in scene 153/83 of the 2009 film Star Trek. 
This is a list of individuals known to exist both in the original and in the alternate reality.
The Star Trek screenplay contains a musing from Spock Prime, having been told by Kirk that Chekov, Sulu, and Uhura were all serving in the Enterprise (by this point he takes it for granted that McCoy is as well), while Scott is on the same planet as the two of them, that Kirk's implausible meetings with the people who would become his crew in the prime reality may be the result of the timeline trying to "repair itself" from Nero's damage. The novelization of Star Trek by Alan Dean Foster preserves this exchange.
Writers Mike Johnson and Tim Jones wrote Star Trek: Countdown, a comic book prequel to Star Trek expanding on the events in the prime reality leading to the Narada's arrival back in time. Johnson and Jones subsequently collaborated on Star Trek: Nero, based on the deleted scenes regarding Nero's imprisonment, and Star Trek: The Official Motion Picture Adaptation. Johnson writes the Star Trek: Ongoing comic series, launched in September 2011, which explores how some classic stories unfold in the new timeline. In early 2013, Mike Johnson and Roberto Orci once again collaborated on the tie-in prequel comic Star Trek: Countdown to Darkness which covers the events that occurred roughly a month before Star Trek Into Darkness and also reintroduces famed captain Robert April (β) in the new timeline.
Four novels set after Star Trek were set to be published in 2010: Refugees, Seek a Newer World, More Beautiful Than Death, and The Hazard of Concealing. The novels were announced as being on hold as of 14 January 2010. On his blog, Refugees author Alan Dean Foster speculated the hold was due to the plots of the novels possibly conflicting with the next film. Two years later, Christopher L. Bennett posted "All I can say is that most of the speculations I hear about why the books were pulled are wrong. It wasn't about conflicts with the second movie."  A series of young adult books, Star Trek: Starfleet Academy, following the characters during their time at the Academy, began in November 2010.
In The Needs of the Many, a novel based upon the Star Trek Online series, when Dulmur, one of the Department of Temporal Investigations agents from DS9: "Trials and Tribble-ations", is institutionalized and suffering from temporal psychosis, he has memories of not only his timeline, but of several others as well – including one where Vulcan was destroyed a century prior. Another novel, Watching the Clock, goes into detail about how and why some forms of time travel create parallel alternate realities and others lead to the overwriting of the same timeline. Bennett, the author, stated this was an in-universe explanation for the co-existence of the prime and alternate realities. 
- Wired: "When Worlds Collide: Spock Confronts the Ultimate Challenge"
- IDW Publishing:
- Star Trek D-A-C
- Star Trek: Expeditions
- Star Trek
- Star Trek: Rivals
- Star Trek Online
- Star Trek: Bridge Crew
- Star Trek: Fleet Command