Coridan was an inhabited Federation planet in the Coridan system of the Alpha Quadrant, and homeworld of the Coridanites, a warp-capable humanoid species. As of 2151, the planetary government was headed by an elected chancellor.
In 2151, Coridan had a population of three billion, with the majority living in several cities in the equatorial region. The capital city was surrounded by a shanty town, and there were almost as many bio-signs outside the city as there were within it. The planet was known for having the largest shipyards in its sector, building advanced warp-capable vessels, some of which were rumored to reach warp 7. However, Coridan was also embroiled in an internal conflict between the government, backed by the Vulcan High Command, and rebel forces, secretly supported by the Andorian Empire. The Vulcan agenda was to keep the planet's chancellorship stable while the Tau Ceti Accords prohibited any Andorian presence on the planet, which in turn assured Coridan's dilithium exports to Vulcan. (ENT: "Shadows of P'Jem")
Chancellor Kalev invited Captain Jonathan Archer and Sub-Commander T'Pol of Enterprise to visit the planet, but they were captured by rebels and held for ransom. As a result, a commando force led by Sopek, the Vulcan senior officer of the sector, as well as the Andorian Imperial Guard, led by Shran, who was thereby violating the Tau Ceti Accords, came to assist the rescue. (ENT: "Shadows of P'Jem")
In 2155, Coridan took part in talks on Earth to form a Coalition of Planets. Here, the Coridanites rejected the Tellarite proposal of a trade embargo against the Orion Syndicate. The Coridan representative claimed his people had been trading with the Orions for centuries and that the accusation of Orions attacking Tellarite freighters was slander. (ENT: "Demons")
Over the next century, Coridan became under-populated to the point that it could not defend its dilithium mines.
In 2268, Coridan sought admission to the United Federation of Planets. However, due to the wealth of minerals available on Coridan and the presence of illegal mining operations, Coridan's admission was a controversial subject between Tellarites and Vulcans. The Babel Conference was convened to settle the matter and ultimately approved Coridan's admission, although Orion smugglers initially tried to sabotage the meeting. Ambassador Sarek of Vulcan was credited with achieving the consensus towards admitting the planet to the Federation. (TOS: "Journey to Babel"; TNG: "Sarek")
During the Dominion War, Coridan's dilithium mines came under attack by the Dominion in 2374, due to their strategic importance. Gelnon left Kudak'Etan in command of the USS Defiant while he and his ship left to launch an attack on Coridan. (DS9: "One Little Ship")
This planet's quadrant of origin is inferred based on the position of its primary Coridan as seen in the star chart appearing in the Star Trek: Discovery episode "Magic to Make the Sanest Man Go Mad".
In the first draft script of "Shadows of P'Jem" (written while the episode had the working title "Untitled Andorians Return"), the capital city of Coridan was referred to, in dialogue, as "an architectural marvel" and, in the stage directions, as featuring "crystalline, high-rise buildings," which Archer speculated "must be a half-kilometer tall." The planet was spoken about as having "fabrication facilities" better than any on Earth. In the stage directions from the same early script, the planet was also described as having a "cloud layer" whose coloration wasn't identified, to be depicted on "a bright, sunlit day." However, in the final draft of the script, Coridan was instead described as having gray clouds and a "crystalline city," with the other descriptions no longer included in the script.
In a deleted scene from Star Trek Into Darkness, a news feed announced that Magustav Pachangara became the new chancellor of Coridan. Information on this planet appeared in a powerwall in the office of Admiral Alexander Marcus. 
According to Star Trek: Star Charts (p. 53) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Coridan (Coridan III) was an M-class planet governed by the People's Republic of Coridan (β) from its seat at New Coridan (β). The dominant species were the humanoid Coridanites, who were warp-capable in 2093. In the mid-22nd century, the planet had a population of three billion. By the mid-23rd century, a centuries-long civil war had reduced the population. In the late 24th century, the planet had a population of 185 million.
In the non-canon novel The Good That Men Do, Coridan was referred to as "Coridan Prime", on the verge of developing warp-7 technology. To prevent such advances from spreading to other Coalition of Planets member worlds, the Romulans launched a vicious attack on Coridan, flying a vessel into the planet at maximum warp. Anti-matter from the suicide attackers' ship mixed with Coridan's abundance of dilithium, causing a fireball that spread across the planet, killing billions. The planet's population was said to be further depleted by civil wars that continued after the Romulan attack.
In Star Trek: The Original Series - Core Game Book, Coridan is described as a cold, dry, class-M world, with a chronically corrupt government, in the 2260s.