The militarization conspiracy was a plot by Admiral Alexander Marcus and Section 31 to militarize Starfleet to prepare for war against the Klingon Empire. To realize his goals, Marcus sought to use the savage intellect of the revived war criminal Khan Noonien Singh. When this backfired with tragic results, Marcus went to extreme lengths to cover up the conspiracy, all while exploiting an opportunity to trigger his war.
Admiral Alexander Marcus, the head of Starfleet in the mid-23rd century, had long been dissatisfied with the Federation's response to the belligerent Klingon Empire. Believing war with the Klingons to be inevitable, he sought to unilaterally transform Starfleet into a military organization. Marcus found the secretive, security-minded Section 31 a willing ally for his conspiracy.
Following the loss of Vulcan in 2258, Starfleet began scouring deep space for new resources and came across the SS Botany Bay, containing 73 augmented Humans from the 20th century in cryogenic stasis. Marcus woke their leader, Khan Noonien Singh, and held Khan's crew hostage to extort him (under the alias "John Harrison") into designing new ships and weapons. Foremost among these efforts was the powerful Dreadnought-class warship USS Vengeance, built by Section 31 at the Io Facility. Disgruntled, Khan attempted to smuggle his crew to safety by concealing them within advanced long-range torpedoes he had designed. However, he was discovered and forced to flee alone.
Believing that Marcus had made good on his threat to kill Khan's crew, Khan plotted revenge on Starfleet. He approached Section 31 officer Thomas Harewood, whose daughter was terminally ill, and offered to save her life if Harewood would destroy a Section 31 facility in London. After Khan fulfilled his part of the bargain, Harewood did likewise by detonating a bomb disguised as his Starfleet Academy ring, killing himself and 41 others. In the ensuing chaos, Khan salvaged a portable transwarp beaming device from the rubble.
The bombing mandated a meeting of Starfleet's senior leadership at the Daystrom Conference Room in Starfleet Headquarters, where Marcus declared a manhunt for "Harrison". Having anticipated just such a meeting, Khan commandeered jumpship 208 and attacked, killing Christopher Pike and several other officers before he was forced to withdraw by James T. Kirk. Khan escaped via transwarp beaming to the uninhabited Ketha Province of Qo'noS, where Starfleet ostensibly could not follow.
Path to war
Devastated by Pike's death, Kirk implored Marcus to authorize an off-the-book mission to pursue Harrison. Marcus saw in Kirk the opportunity to eliminate Khan, cover up his conspiracy, and incite war with the Klingons on his terms, all in a single stroke. Marcus instructed Kirk to take the USS Enterprise to the Klingon Neutral Zone and kill Harrison using 72 long-range torpedoes, which he knew contained Khan's crew. He also arranged for the sabotage of the Enterprise's warp core, which would leave her stranded when the Klingons came to investigate the source of the torpedoes; war would undoubtedly follow.
Enterprise first officer Spock strongly objected to executing Harrison without trial, and ultimately prevailed on Kirk to arrest Harrison instead. Despite the failure of the Enterprise's warp drive, Kirk decided to proceed with the mission. On the surface of Qo'noS, the Enterprise away team ran afoul of a Klingon patrol, who were in turn slaughtered by Harrison. Harrison then surrendered himself, inferring correctly that his crew was still alive from the presence of the torpedoes on the Enterprise. Kirk sent a message to Starfleet informing them that he had Harrison in custody, inadvertently alerting Marcus that he was in danger of being exposed.
Aboard the Enterprise, Harrison revealed his true identity and his involvement with Marcus. At his urging, Leonard McCoy and Carol Marcus opened a torpedo and found one of Khan's crew inside. Khan also gave Kirk the coordinates of the Io Facility, which Kirk passed to Montgomery Scott on Earth. Scott arrived at the drydock as the Vengeance was preparing to launch, and sneaked aboard.
Battle over Luna
Marcus, commanding the Vengeance, confronted the Enterprise at the edge of Klingon space and ordered Kirk to hand over Harrison, to which Kirk demurred. After Kirk revealed his knowledge of Khan's crew, Marcus concluded that everyone on the Enterprise needed to be silenced.
The Enterprise raced for Earth, bringing evidence of Marcus's conspiracy. However, the technologically superior Vengeance overtook the Enterprise and forced her out of warp near Luna with a phaser barrage, 237,000 kilometers short of Earth. Marcus rejected Kirk's plea for mercy and prepared to destroy the Enterprise, only to find the Vengeance's systems disrupted from within by Scott. The temporary lull allowed Kirk and Khan to board the Vengeance in environmental suits.
Kirk, Scott, and Khan made their way to the Vengeance bridge and seized control, though Marcus remained defiant. Khan promptly turned against Kirk, overwhelmed his team, and murdered Marcus. He then demanded that Spock surrender his crew or face destruction. Spock complied, allowing Khan to transport the 72 torpedoes to the Vengeance in exchange for Kirk and the others. Khan opened fire on the Enterprise, unaware that Spock had foreseen his treachery and armed the torpedoes, after McCoy removed the cryo-tubes. The explosion of the torpedoes crippled the Vengeance.
The two starships, both critically damaged, were caught by Earth's gravity and began falling toward the surface. Kirk managed to reactivate the Enterprise's warp core in time to avert a crash, suffering fatal radiation poisoning in the process. Khan, believing his crew dead, directed the Vengeance to crash into Starfleet Headquarters in a final act of spite. The enormous ship plowed through San Francisco, obliterating landmarks like Alcatraz Penitentiary and killing many civilians before coming to a rest.
Khan survived the crash and leaped from the wreck in a bid for freedom. Spock pursued him with the intent of killing him to avenge Kirk's death. The two fought, though Khan eventually gained the upper hand. Meanwhile, McCoy realized that Khan's blood could be used to revive Kirk. Nyota Uhura beamed down and stunned Khan repeatedly, allowing Spock to defeat and incapacitate him.
Nearly a year later, Kirk spoke at a memorial for the lives lost as a result of Khan and Admiral Marcus' actions. In his speech, Kirk reminded the attendees that Starfleet's true mission was the exploration of the galaxy. Shortly afterward, he returned to the Enterprise, to begin the first five-year mission. (Star Trek Into Darkness)
The conspiracy ultimately failed since, as Montgomery Scott once stated, Starfleet was not a military organization. (Star Trek Beyond)
Co-writer Damon Lindelof said the militarization plot in Star Trek Into Darkness came about because they needed to acknowledge the events of Star Trek, but "obviously we don't want Starfleet to militarize, so that's going to be the force of antagonism in the movie, is that that's happening, either in secret or openly." The protagonists, the Enterprise crew, would then "have to sort of make an argument against militarization. That being said, that's going to be a hard argument for them to make, because maybe Starfleet should be militarizing. So the bad guy in the movie is going to be a guy who's, like, going one step too far."
Furthermore, it enabled them to bring in Khan in a new way: "The whole reason that we're doing these movies is these things are unfolding somewhat differently. So wouldn't it be cool if Khan actually got woken up before this movie started, and he's in play? Once we came upon that idea, then it became absolutely mandatory to call him something else, because if Kirk and the crew of the Enterprise didn't know who this guy was or were being lied to about his identity, we needed to replicate that process for the audience." 
The storyline had real-life parallels to the miltaristic response of President George W. Bush to 9/11. "All that stuff was in the air and I think we weren't trying to make a sociopolitical statement when we wrote the story, but we just started gravitating towards those ideals because that’s what was on the news," said Lindelof.  Actor Simon Pegg felt "There is a parallel with the terrorist activities of Osama Bin Laden and the decision to attack Iraq. Iraq had nothing proven to do with 9/11, and yet Bush used that as an excuse to start a war with those people." He also compared Marcus to Bush's vice-president Dick Cheney. 
The Star Trek: Countdown to Darkness comic book series and subsequent issue "Star Trek After Darkness, Part 1" reveal the Mudd Incident was an early attempt to start the war with the Klingons: Robert April would take over the Enterprise, and thereby begin the war by handing the flagship to Kor.