The Domain was a collective intelligence that the Forerunners used to access the ancient ancestral knowledge of their forefathers. The Domain was only accessible by adult Forerunners through their armor because only the adults were able to comprehend the knowledge which was fed directly into their central nervous system.
Unknown to the Forerunners, the Domain was created originally by the Precursors after they cultivated massive amounts of knowledge throughout multiple galaxies to be stored within the Milky Way. The Domain was sustained and protected by Precursor architecture, which was neurophysical and therefore vulnerable to the firing of the Halo Array.
With the Domain destroyed, the monument and testament of the Forerunners' crimes and redemptions would be lost forever. Ur-Didact was asleep within his Battle Cryptum and could not enter the Domain, so he was condemned to spend millennia of silence and darkness with his own insanity.
The Domain was also the Organon, a device long sought after thought to be able to activate all Precursor artifacts in the Galaxy. As the Domain was the knowledge of the Precursors, the knowledge of how to activate and control the Precursors' neurophysical technology would logically be hidden there.
Despite its apparent destruction with the firing of the Halo rings, some aspect of the Domain remained active on the planet Genesis, a planet devoted to connecting the extant realm with the digital Domain. It was here that Cortana took charge of the Mantle of Responsibility, and began her usurpation of the galaxy's sovereignty.