The Hall of Souls was a device created by Adrian Veidt shortly after his attack on New York in the original Watchmen. Paranoid and fearful that his scheme would be uncovered, he built himself a secret cloning facility deep under Karnak, with the idea of transferring his consciousness into a new body should anything happen to him.
The existence of the device was first mentioned in the "Death of Our Souls" arc in the second volume, where Adrian Veidt (later referred as "Adrian Alpha") was killed in a fight with a giant gorilla on the Moon.
This was a story device that was never really explained or built upon, and it has never actually been seen in the comic. It would appear to be just a plot device that the writers can rely on to make sure that there is always an Adrian Veidt to antagonize the rest of the cast.