The Jedi Temple on Coruscant was the headquarters of the Jedi Order from the conclusion of the Great Sith War to the Great Jedi Purge and during that time was home to its major training, bureaucratic and dormitory facilities. Jointly operated by the Order and the Galactic Republic, the Temple was sealed to all but the Jedi and their allies, with very few public areas.
The Jedi Temple on Coruscant was originally built over an ancient Sith shrine in the hopes of sealing away the traces of the Dark side of the Force that emanated from the site, as well as taking advantage of the wellspring of Force energy that emanated from the area. Over time however, as the Dark side grew stronger, the evil aura of the Sith shrine seeped up into the temple, making it more and more difficult for the Jedi to foresee the future and weakening them.
The complex would be abandoned and largely destroyed at the time of the Declaration of a New Order when the Order by the Galactic Empire. When he became emperor, Palpatine converted the temple into his own personal palace. The building was rebuilt into an amalgam of dark colored, blockish edifices with sloping facades, with only the old spires rendered unharmed.
In Star Wars Rebels and The Force Awakens, it is revealed that the Jedi Temple on Coruscant; is not the only Jedi Temple in existence, as there are several Jedi Temples throughout the galaxy, like the Jedi Temple on Lothal and the First Jedi Temple on Ahch-To, these temples were all believe to have been destroy in the Great Jedi Purge, however, there are still several Jedi Temples that still exists; these temples serve as Jedi academies to train new generations of Jedi Knights across the galaxy.