Coruscant doesn't even gets a mention in the first three films produced ( eps. IV, V, VI ) but plays a major part in the second trilogy ( I, II, III ). All scenes and any mentioning of the planet in the original trilogy was added for the updated version in the late nineties.
Coruscant is the heart of the star Wars galaxy, the place where the Emperor Palpatine reigns from. Before the Emperor came to power, it was the home for the Jedi Council and the Grand Assembly, something like the United Nations building in New York.
The planet was created by Timothy Zahn for his Admiral Thrawn trilogy. Lucas liked the planet and it became central to the second three films. The scene set on Coruscant in the original series was added for the edited films in the late nineties.
The natural woodland and features had long gone before any of the stories that were set on the planet. It is not know what the original atmosphere and environment was, was the planet a desert world like Mars and then terrformed to be breathable or was it like Earth and just built over.
The Jedis are followers of the Force who keep order across the galaxy. Their galactic headquarters is the Jedi Temple. At the top of one of the towers is where Mace Windu and other Jedi Masters confer.
The Jedi Temple contains a large database of everything to do with the galaxy. The security of the database is lacking when someone is able to delete the location of Kamino forcing Obi-Wan Kenobi to take a chance on the location of the planet.
When Palpatine takes control of the Senate, Anakin Skywalker leads a group of Clone Stormtroopers to kill all the padawans that are learning there. Senator Bail Organa arrives at the Jedi Temple when the assault is underway but is powerless to intervene and leaves.
The Senate is where representatives from the known worlds meet to discuss the events that are effecting the galaxy. When Vice-Chancellor Finis Valorum is ineffectual in dealing with the crisis on Naboo, a vote of confidence is called and Valorum looses resulting in the rise of Palpatine.