The anti-matter universe was the universe in which Omega was trapped and ruled over. It was situated in a black hole, leaving it a pocket universe. Omega was able to shape this universe as he saw fit, creating his own paradise in which to dwell.
Over the centuries, he grew despondent due to his isolation, and the landscape slowly became unstable because of this. Omega planned to escape the anti-matter universe and return to his original reality. The universe had a corrosive effect, causing Omega's physical body to wear away. (DW: The Three Doctors, Arc of Infinity) It could also be accessed by way of Zeta Minor, the last known planet in the universe. (DW: Planet of Evil)