The Colonial Defense Mainframe was the high-security central computer where it's presumed all Colonial fleet data, logistics, strategies, and software are managed, stored, tested, and disseminated. It is presumed that the Defense Mainframe resided in, or was accessible from Caprica City.
Two years prior to the events in the Mini-Series, scientist Gaius Baltar allowed a fellow programmer and love interest to rewrite many of the system's algorthms and other programming in coordination with his fleet software upgrade, the Command Navigation Program, which was distributed and installed on almost all ships in the Colonial fleet.
Baltar discovered later that his love interest was a humanoid Cylon spy, model Number Six, who used Baltar to gain access to the entire Colonial defense network through the mainframe. As a result, his Command Navigation Program was rife with programming backdoors that allowed the Cylon fleet to use viruses or system commands that shut down almost all Colonial ships, from fighters to battlestars during the Fall of the Twelve Colonies.
Battlestar Galactica's computer systems were never networked, nor was the CNP installed to any of its subsystems. Her last Viper Mark VII squadron did have the CNP loaded, which led to their immediate destruction by two Cylon Raiders in the early moments of the attack.
According to Shelly Godfrey, the Defense Mainframe was destroyed by an explosive device, ostensibly placed there by Gaius Baltar, moments before the Cylon Attack (Six Degrees of Separation).