- You may be looking for the research facility of the same name.
The Edge was a symbolic, metaphysical place in the Doctor's mind where each incarnation went before regeneration, guarded by "vestiges of [the Doctor's] consciousness" from their past, who manifested as the Guardians of the Edge. When asked what the Edge was the edge of, the Guardians' Eighth Doctor manifestation replied "Existence."
The Thirteenth Doctor's consciousness found itself at the Edge after the Spy Master enacted the Thirteenth Doctor's forced regeneration. According to the Fifth Doctor manifestation, the literal ravine's-edge she viewed was "obviously" symbolic because "consciousness will do that", but he also explained that in a very real sense, passing across the ravine would seal the process of regeneration, after which would be "no way back". However, as a show of "strength of character", the manifestation of the Thirteenth Doctor refused to pass through the Edge, meaning it was possible for Yasmin Khan, Inston-Vee Vinder and the Holo-Doctor to work together to degenerate the Doctor's body back to their Thirteenth self and eject the Master's soul, restoring the Thirteenth Doctor to the physical world. (TV: The Power of the Doctor)
Similar events[]
In a dream, the Fourth Doctor encountered his previous incarnations in a heavenly garden, which made him aware that his own regeneration was on the horizon. (PROSE: Into the Silent Land)
During the Seventh Doctor's battle with the Timewyrm, Ace entered the Doctor's mind, encountering various past Doctors in various guises, including the First, Third and Fourth Doctors. She discovered the Fifth Doctor had become symbolic of the Doctor's conscience and freed him from the confinement the current Doctor's persona had put him in so he could what he believed was necessary to stop the Timewyrm. (PROSE: Timewyrm: Revelation)
The Eighth Doctor found himself in a metaphysical place after he was stabbed and killed by his companion Charley Pollard. There he talked with previous three incarnations, who judged him on his death, before helping him to summon Zagreus to inhabit their body to ensure that the Doctor would not die for good. (AUDIO: Zagreus)
The Tenth Doctor encountered his next incarnation in a dream, assuring him that they would both be fine. (COMIC: To Sleep, Perchance to Scream)
Additionally Clara Oswald encountered ghosts of the Doctor’s past incarnations, including the First Doctor, the Fourth Doctor, the Fifth Doctor, the Sixth Doctor, the Ninth Doctor and the War Doctor, in a nowhere land in the Doctor’s timestream. (TV: The Name of the Doctor)