Throughout much of Star Wars history, Coruscant was the most important planet in the galaxy. Made up of a huge, sprawling city, it was located at the center of the galaxy both literally and figuratively, serving as the capital for numerous governments and the center of many trade routes.
Early History
Coruscant was once covered in oceans and inhabited by an indigenous race, the Zhell. The Taung race invaded the planet around 200,000 BBY, but the Zhell eventually drove them off.
By 100,000 BBY, the planet had evolved into a giant city, with new buildings constructed on top of the old until the land -- and the lower levels of the city -- became completely hidden from sunlight. At its height at the end of the Clone Wars, the planet was home to one trillion beings according to official records, but possibly as many as three trillion beings altogether.
Galactic Capital
When the Galactic Republic was established in 25,053 BBY, Coruscant became its capital. The hyperdrive was still a relatively new technology, and Coruscant was at the center of many developing trade routes -- and a target for attack in many battles. After the end of the Great Sith War in 3,996 BBY, the Jedi Council relocated from Ossus to Coruscant, where they remained for nearly four thousand years.
Emperor Palpatine established the Galactic Empire in 19 BBY and renamed Coruscant "Imperial Center." The Rebel Alliance finally managed to retake Coruscant in 6.5 ABY, two and a half years after their victory over the Emperor at Endor, as the capital of the New Republic. This was a moral victory as well as a strategic one, leading to further infighting and fragmenting amongst the Imperial Remnant.
Yuuzhan Vong War
After briefly losing Coruscant to the Imperials in 10 ABY, the New Republic held the capital until the height of the Yuuzhan Vong War. As a planet-wide city, Coruscant was a symbol of the artificial technology the Yuuzhan Vong hated, and in 27 ABY they captured the city and used terraforming to restore its natural ecosystem.
In the aftermath of the war, the new Galactic Alliance decided to keep Coruscant as their capital, restoring the original cityscape wherever possible. The planet remained the galactic capital through the rise of the Fel Empire and Darth Krayt's Sith Empire in the 130s ABY.
Behind the Scenes
Coruscant was originally named "Alderaan" in early drafts of A New Hope and "Had Abbadon" in early drafts of Return of the Jedi; both names were later used for other planets in the Star Wars universe. The Star Wars RPG books by West End Games listed the Imperial capital's name as simply "Imperial Planet."
Timothy Zahn named the planet Coruscant in The Thrawn Trilogy, on the grounds that "nobody names a planet 'Imperial Planet.'" The name comes from the Latin "coruscare" ("to sparkle/to glitter") and was pronounced "ko'-ru-skant'." Lucas added the name to the films in the Return of the Jedi Special Edition and the Prequel Trilogy, but changed the pronunciation to "ko'-ru-sant'."
The possibility of a planet-wide city with little water and no arable land poses huge practical problems, making a planet like Coruscant impossible in real life. Irregular Webcomic! humorously addressed the problem of food production, noting that Coruscant would require "the entire output of 10,000 agricultural planets," flown in daily by 80,000 Super Star Destroyers, to feed all of its residents.