This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
(covers information from several alternate timelines)
Andoria or Andor was an inhabited moon orbiting a ringed gas giant of the Andorian system. Andoria was the homeworld of the Andorian and the Aenar races, and was a key world to the United Federation of Planets.
Andoria was located in a neighboring system to Vulcan. Regulus, which was relative to both planets, laid just outside Andorian sensor range. (ENT: "Kir'Shara") The planet Weytahn, located on the frontier between the Vulcan and Andorian systems was located "a dozen light years" from Earth. (ENT: "Cease Fire") The Andorian Empire occupied space between Babel and Tellar Prime. (ENT: "Babel One")
During the 24th century, Andoria was located near to the Cardassian border. (DS9: "Tears of the Prophets") Following the Dominion invasion and conquering of Betazed, they were in a position to threaten Vulcan, Andor, Tellar, and Alpha Centauri. (DS9: "In the Pale Moonlight")
In 2293, the location of Andor in the Milky Way Galaxy was labeled in the star chart The Explored Galaxy, which was on display in Captain James T. Kirk's quarters aboard the USS Enterprise-A. (Star Trek VI: The Undiscovered Country, okudagram)
In 2366, in an alternate timeline, during the Federation-Klingon War, the location of Andor was labeled on a tactical situation monitor in the ready room aboard the USS Enterprise-D. (TNG: "Yesterday's Enterprise", okudagram)
In 2399, the location of Andoria was labeled on a star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters. This planet was located in or near to Federation space. (PIC: "Maps and Legends")
There was contact between the Andorians and the Aenar in the distant past, but eventually communication ceased and the two races came to remember the other only in myths and stories. It was not until around 2104 that contact was re-established between them. (ENT: "The Aenar")
The moons of Andoria were among multiple locations that could be experienced in a 2256 demonstration of the possibilities of spore drive; that year, Captain Gabriel Lorca pointed out to Michael Burnham that, while journeying on the mycelial network, a traveler might blink and, before they knew it, they were visiting the moons of Andoria. (DIS: "Context Is for Kings")
In a commercial for Tribbles cereal, Andoria was shown on a computer screen of a food synthesizer in the mess hall of the USS Ravenous. It was listed along with other locations such as Earth, Vulcan, Izar, Cestus, Tellar, Rigel VI, and Rigel X. (ST: "The Trouble with Edward", credit cookie)
Sometime before 2363, Lisa Cusak, as a junior officer, was assigned as an attaché to the Federation embassy on Andor. She met an Andorian civilian who worked at the Andorian Agricultural Ministry. The two ended up dating for six years. (DS9: "The Sound of Her Voice")
In 2373, Kai Winn rhetorically asked Captain Benjamin Sisko if the Federation would be willing to sacrifice Andor, Vulcan, Berengaria, or even Earth to protect Bajor from the Dominion, if necessary. (DS9: "In the Cards")
In a possible 3186 experienced by Gabrielle Burnham, Andoria was one of the worlds where all life had been eradicated using antimatter detonations, apparently by Control. Traveling back to 2257, she communicated her memories to Spock, who later shared them with Michael Burnham. (DIS: "If Memory Serves", "Perpetual Infinity")
In the mirror universe, Andor was a dominion of the Terran Empire by 2256, when Terran emperor Philippa Georgiou held the title Regina Andor. She later offered Eling a position as governor of Andor. (DIS: "Vaulting Ambition")
Climate and geography
Andoria was an ice world, with a Human-breathable oxygen-nitrogen atmosphere. A specially designated Andor Environment Ward was located at Starbase 515 in 2365. (TNG: "Samaritan Snare") According to Thylek Shran, "when a Guardsman dies far from home, [their] companions carry part of [them] back to the ice of Andoria." (ENT: "United")
Only during rare heatwaves would the temperature on Andoria rise above freezing, and even then only for a few weeks at a time. In the northern wastes, a temperature reading of -28° was not uncommon during mid-summer. (ENT: "The Aenar")
Points of interest
Flora and fauna
"an-DOOR" was the pronunciation for this planet's name from the script pronunciation guide for "In the Cards". 
A newspaper article (It's Federation Day!) in the Picard family album, created for Star Trek Generations, suggests that a "Sarahd of Andor" was the Andorian representative present at the forming of the Federation in 2161, though the clipping was not seen on screen and is not considered canon.
In the final draft script of ENT: "Fight or Flight" (dated 1 May 2001), Andoria was referred to as having once been visited by Travis Mayweather and his family aboard their ship. However, this reference was later changed to Lavinius (by or on 27 June 2001, when a revised final draft of the script was issued), and the scene was ultimately deleted.
While Star Trek: Enterprise portrayed Andoria as a moon, Gabriel Lorca mentions "the moons of Andoria" in DIS: "Context Is for Kings", which appears to establish that Andoria had its own system of moons. Moons around moons are currently believed to be theoretically possible, but not stable, due to tidal forces causing them to de-orbit.   Lorca may have alternatively been referring to other moons within the Andorian system.
Depiction on Enterprise
The Star Trek: Enterprise episode "The Aenar" finally established the often spoke of Andorian homeworld as a moon, orbiting a gas giant. This was devised by Judith and Garfield Reeves-Stevens as an attempt to help explain the contradiction of why it was sometimes called Andor and sometimes it was called Andoria, the gas giant being Andor and the moon Andoria. (ENT Season 4 DVD special features; Star Trek: The Official Starships Collection, issue 37, p. 14) While a shot of the planet seen in "The Aenar" thus appears to depict Andoria as a moon of the much larger planet close by, this is never explicitly stated in the episode. This would, however, seem to contradict Worf's claim in "Change of Heart" that Andor has mountains.
Alternately, Michael and Denise Okuda have suggested that Andor and Andoria are the same, with Andor being the preferred name on Star Trek: Deep Space Nine. ("The Andorian Incident", text commentary, ENT Season 1 DVD special feature)
The Last Unicorn Games Star Trek RPG and Samuel John Ross used information about Andoria, a frozen world first published in Star Trek: The Role Playing Game, for the work The Andorians: Among the Clans. Having been reading this publication, Mike Sussman was inspired by the book's cover while working on Star Trek: Enterprise. He later stated, "I remember saying to Manny Coto, who was our season 4 showrunner, 'What do you think of this as a look for the Andorian homeworld?'" (Star Trek: The Official Starships Collection, issue 37, p. 15)
Mike Sussman's suggestion addressed a need to save expenses, as caverns built for an ENT Vulcan trilogy, which had recently wrapped production, could be reused as the Andorian ice caves, simply repainted white. The fact that the sets could be redressed in such a way was one motive for pursuing the idea. Remembering Manny Coto's response to the plan, Sussman relayed, "He said, 'Great, because we can paint our Vulcan sets white and now it's ice!' and that's what we did." (Star Trek: The Official Starships Collection, issue 37, p. 15)
In the final draft script of "The Aenar", Andoria was described as "an icy, M-Class world" with "a stark yet stunning arctic landscape, lit by brilliant sunlight with a slightly bluish hue." The planet was also referred to as having "a driving, howling wind."
Andoria was shown using various methods. "Herman Zimmerman and his team at the art department made wonderful ice cave sets," said Visual Effects Producer Dan Curry. "For the exteriors we used a combination of matte paintings." (Cinefantastique, Vol. 37, No. 2, p. 40)
A particular set that was used as Andoria could be paid for over a longer stretch of time than the Star Trek TV series usually allowed. "We, you know, were able to build a huge set of Andoria," Manny Coto recalled. "And because we played that set over various episodes, we were able to amortize the building of the set and get bigger production value." ("Before Her Time: Decommissioning Enterprise, Part Two: Memorable Voyages", ENT Season 4 Blu-ray special features)
The Star Trek Encyclopedia (4th ed., vol. 1, p. 24) identifies the gas giant as Andor. Both StarTrek.com and the Star Trek Encyclopedia state that "Andor" was a name which was used interchangeably with Andoria for the Andorian homeworld. The former source does not name the gas giant.
According to Star Trek: Star Charts, Andor was the capital city of Andoria, which was a class M planet. According to Star Trek: Star Charts (pp. 36 & 52; "United Federation of Planets I"), Andor was the eighth planet in the Andoria (Procyon, or Alpha Canis Minoris) system. Its moon Andoria was depicted as an Earth-like planet.
According to Star Trek: Star Charts (pp. 19, 36, 52 & 60), Andoria was a class M planet located in the Procyon binary star system. This system consisted of an F-type main-sequence star orbited by an A-type main-sequence star, with Andoria identified as the eighth planet. It was the capital of the Andorian Empire, and a founding member of the United Federation of Planets in 2161. The capital of Andoria was Andor, and 38.2 billion people lived on Andoria. Andorians became warp-capable in 1154 AD. Andoria was located in the Andorian Sector, also known as Sector 006. This sector was the sixth explored by Earth ships. In his final voyage in 2120, Zefram Cochrane visited Andoria.
According to Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), "Andor" was an alternative name for Andoria (as was "Procyon VIIIA") but was also a Class J gas giant, of which Andoria was a moon.
According to the more recent Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Andoria was the first moon in Andor's system. The gas giant Andor was the eighth planet in the Andoria (Procyon) system. The depiction of Andoria was closer to its appearance in "The Aenar".
According to Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Andoria (Andor, or Procyon VIIIA) was a moon of Andor. It was the capital of the Andorian Empire, and a founding member of the UFP in 2161. The capital of Andoria was Laikan. The primary species were Andorian and Aenar. In the late 24th century, there were 1.8 billion Andorians and 4.1 million Aenar living on this moon. Andoria became warp-capable in 1154 AD. In his final voyage in 2120, Zefram Cochrane visited Andoria.
According to the Star Fleet Medical Reference Manual and The Worlds of the Federation, Andor was the eighth planet in the Epsilon Indi system. It was called "Fesoan" by its natives. In the Star Fleet Medical Reference Manual and in Star Trek Maps, Andor was referred to as the Andorian homeworld.
According to the RPG sourcebook Planets of the UFP, Andor was the fifth planet orbiting the star Kuy'va.
In Worlds of Star Trek: Deep Space Nine, Volume One, Thirishar ch'Thane and Prynn Tenmei note the differences between the names "Andor" and "Andoria". While Tenmei grew up thinking of ch'Thane's homeworld as "Andoria", ch'Thane grew up knowing it as "Andor". Conversely, ch'Thane grew up thinking of Tenmei's homeworld as "Terra", only to discover that Terrans call it "Earth".
In the novel Lost Souls, much of Andor was devastated by the Borg in 2381. The following year, Andor seceded from the Federation in Paths of Disharmony, although it was later readmitted as a result of the events of Star Trek: The Fall.