Black Void

The Black Void was a "howling emptiness" existing outside of the universe, at the "very edge of Time and Space". It was "the canvas on which reality was painted". It was also "a place where things that didn’t exist howled and raged against their nothingness". (PROSE: Past, Present & Yet To Come)

Nature
The Black Void was the void that existed before the Big Bang and was being filled out by it, space without any kind of matter or energy. On the edge of the universe one could see quasars and other forms of cosmological expansion happening. (PROSE: Fear of the Dark) the Dark existed in the void before the Big Bang. (PROSE: Fear of the Dark)

The Black Void also existed once again at the end of the universe as its natural endpoint. Positioned just before the end of Time itself was a liminal span of existence called the Boneyard, overlooking the Black Void, which was a place where the heroes of the universe came to die peacefully.

The Black Void was actually sentient and tried to enter the universe and "optimise" it to its needs, constantly rewriting the timeline of its physical embodiment to optimise itself to shifting conditions, and "optimising" the timelines of other individuals. It was ultimately tricked and defeated by the Crone, Lucy Wilson's distant future self, who cast it back out of the world at the very end of the universe; due to its own timeless nature, this was also the very banishment that had placed the Black Void at the beginning of the universe in the first place. (PROSE: Past, Present & Yet To Come)

History
The Black Void was the void that existed before the Big Bang. Over the course of Time, the universe slowly expanded into that void. (PROSE: Fear of the Dark)

After arriving in the White Void located "outside" of the Land of Fiction, which the Second Doctor stated was "nowhere" and outside of time and space, an intelligence believed to be the Master of the Land attacked the Doctor's mind as well as his companions Jamie McCrimmon and Zoe Heriot. The TARDIS relocated to the black void, where it turned over and over before losing its dimensional transcendence and breaking apart as six sides of a police box. The Doctor drifted away from Jamie and Zoe, who held onto the console before being engulfed in smoke. They eventually arrived in the Land of Fiction. After defeating the Master Brain and causing the Land of Fiction to dissolve, the TARDIS travellers and the Master faded back into the black void where the TARDIS reassembled itself. (TV: The Mind Robber)

The Monk summoned Artemis the Chronovore at the edge of the black void. (PROSE: No Future) Additionally, the Dark existed in the void before the Big Bang. (PROSE: Fear of the Dark)

The Watcher took the Doctor's TARDIS out of space and time, from which Adric and Nyssa would be safe and could observe the entropy wave the Master had unleashed following the destruction of Logopolis. (TV: Logopolis)

The demon Melanicus was trapped in the black, formless void for a thousand years until he escaped through the Event Synthesizer. (COMIC: The Tides of Time)

Behind the scenes
The relationship between the Black Void surrounding the physical univers and the Void (the space between universes, plural) is unclear, no two stories having ever used the two in conjunction. Although at first glance the two might appear to be two names for the same concept, and certainly the two Voids are applications of the same literary tropes, the Black Void appears to merely be the empty space all around the physical universe, whereas the Void Between Worlds is described by the Doctor in TV: Army of Ghosts as containing "absolutely nothing", including "no up, no down (…) no space, no time".