The pre-universe was the universe, perhaps the most recent of many universes, that came immediately before N-Space, the home universe of the Doctor. Like N-Space, magic was a powerful force here, and science did not exist. Unlike N-Space, it was never rationalised, and thus, science never worked, and magic always did.
After the destruction of the Pre-Universe, some species found their way into N-Space and some (such as the Ancient Lights, Great Old Ones and the Beast) had god-like powers. Thus, some of the most powerful beings in existence came from before the universe that was home to the Time Lords began. This made them older even than the Time Lords themselves. (PROSE: All-Consuming Fire, Millennial Rites, TV: The Impossible Planet)
The physics of this universe were different from N-space. Because of new laws like the speed of light or the charge of the electron, the Great Old Ones found they had great power and became terrible gods. (PROSE: All-Consuming Fire) The Shepherd and Shepherdess escaped the extinction of their universe (presumably this one) and arrived in N-space where their appearance became transparent. They moved without touching the ground and their hair and nails grew longer because they were dying in the new reality. (AUDIO: Persuasion)
The Doctor described the pre-universe to Anne Travers.
Before this universe was created, there was another one. A totally different universe, with alien physical laws. The heavens were green, and the stars looked like... giant doughnuts, to be brutally frank. Very, very different. And, as in this universe, there were people who discovered the deeper mysteries of time and space.
Knowledge of this universe was a closely guarded secret. The Doctor only knew about it as a result of his connection to the Matrix during his time as Lord President. (PROSE: Millennial Rites, TV: The Invasion of Time) Even then, the knowledge would have proven temporary: in his sixth and seventh incarnations, the Doctor was fully conversant with the details and specifics of this universe (PROSE: All-Consuming Fire, Synthespians™).
Amongst the races that claimed to be older than the universe itself were the Great Old Ones such as Azathoth, Yog-Sothoth and Shub-Niggurath. (PROSE: All-Consuming Fire, Millennial Rites) On many planets, these beings became part of the legends and religions. The Great Old Ones were worshipped by the first intelligent species to evolve on Earth - the Silurians. (PROSE: All-Consuming Fire) It is unclear whether the Great Old Ones were a single species, or merely a term to describe any unimaginably powerful being that had escaped the Pre-Universe into ours.
The Beast claimed to have originated before the universe and to have been imprisoned by the Disciples of the Light, likely placing both in the Pre-Universe. The Beast was also said to have been the inspiration for all Satan-like figures in the mythology of countless alien races, including the Demons of human mythology, the ancient Kaled God of War and the Draconian God of Evil. (TV: The Impossible Planet / The Satan Pit)