Guardians of the Edge

The Guardians of the Edge were aspects of the Doctor's psyche based on their past incarnations. They appeared as various incarnations and flickered between each other, and sat beside the Edge of Existence, the place in the Doctor's mind where each incarnation went before regeneration, represented by a barren cliff with a telephone pole. Although each Guardian maintained their own individual personality similar to that of the incarnation they appeared to, they acted together as one being. (TV: The Power of the Doctor)

History
When initiated a forced regeneration on the Thirteenth Doctor, he used the regeneration to transplant himself into her body. As the Master became accustomed to the Doctor's body, the Thirteenth Doctor found herself in her own mind, in an arid wasteland with nothing but telephone wires. She then noticed an apparition of the First Doctor wearing black robes with red embroidery, sitting by one of the telephone poles, who remarked that by refusing to "pass through" her incarnation had "quite the strength of character". He then took the appearance of an elderly Sixth Doctor, asking what they would do about the predicament, and that it couldn't be ruined for "the next one". He morphed into an elderly Fifth Doctor to encourage her, and then the Eighth Doctor, who explained they were there to help stop her from going through with the forced regeneration. The Guardians continued to switch between these incarnations and the Seventh Doctor, explaining they were vestiges of the Doctor's past consciousness, the "Guardians of the Edge". The Guardian with the appearance of the Eighth Doctor also noted he refused to wear robes, with the Seventh explaining there was "always one... [who had] to be different."

The Guardians explained that the aforementioned Edge was that of this incarnation's existence, where they come through to pass before becoming the next one, and the point of no return. They reminded the Doctor that time was running out, but their body was still weak from the forced regeneration. As the Doctor realised that this meant it was reversible, she turned in gratefulness to the Guardians for giving her the motivation she needed, only to find the rock they had sat upon was empty. (TV: The Power of the Doctor)

Appearance
The Guardians appeared as older versions of the First, Fifth, Sixth, Seventh and Eighth Doctors. They wore red gowns and black robes, with the exception of the one representing the Eighth Doctor, who wore clothes similar to those he wore before his own regeneration on Karn. They were able to morph fluidly between each other. (TV: The Power of the Doctor)

Behind the scenes

 * While the absence of late Second Doctor, Third Doctor, and War Doctor actors Patrick Troughton, Jon Pertwee and John Hurt was understandable, Fourth Doctor actor Tom Baker was invited to take part in the Special, but was unavailable, with Chris Chibnall explaining "''We asked Tom, but sadly he could not do it. He was not available. Such a shame.".
 * Other accounts have indeed portrayed past incarnations of the Doctor residing within their mind after having regenerated. (PROSE: Into the Silent Land, Timewyrm: Revelation)