Karn was once a colony planet of Gallifrey. It was later was the home of the powerful Sisterhood of Karn and bolt-hole of the Time Lord criminal Morbius.
Characteristics
Following the defeat of Morbius, Karn had become a burned-out and exhausted planet, a barren and rocky wasteland with many ruins and abandoned industrial plantations. It was littered with the wreckage of crashed spaceships from many worlds, brought down by the Sisterhood's telekinetic powers out of fear of theft of the Elixir of Life. (TV: The Brain of Morbius)
The Doctor stated that his birth had taken a few billion miles away and, therefore, by implication, near Gallifrey. (TV: The Brain of Morbius)
History
Prior to the Last Great Time War
Karn was originally a colony of the old Gallifreyan Empire in the days before Rassilon. The Sisterhood of Karn were a remnant of the Pythias who once ruled Gallifrey before being expelled by the triumvirate of Rassilon, Omega, and the Other. (PROSE: Cat's Cradle: Time's Crucible)
During the Rassilon Era, the Sisterhood guarded the Sacred Flame. The Sacred Flame was used to distill the Elixir of Life, which could aid a Time Lord who experienced difficulty with regeneration. (TV: The Brain of Morbius)
Morbius, a renegade Time Lord, in his bid for galactic conquest, came to Karn with a mercenary army. The Time Lords cornered him there, defeated, tried and supposedly executed him. Mehendri Solon, a human surgeon belonging to the Cult of Morbius, removed Morbius' brain and preserved it and vowed to resurrect him. Solon settled on the planet in a disused hydrogen plant and sought a way to make Morbius live again. He used the body parts from dead crew members of different species crashed ships to create a crude, grotesque new body for him.
The Fourth Doctor and his companion Sarah Jane Smith stumbled across this plot after the Time Lords redirected the Doctor's TARDIS to the planet. The Doctor gassed Solon to death and defeated Morbius. (TV: The Brain of Morbius)
During the Last Great Time War
The Sisterhood remained on Karn. Their leader, Ohila, anticipated the Doctor's return in hopes he could stop the war then raging across creation. A gunship containing the Eighth Doctor and the ship's sole remaining crew member Cass crash-landed. The Doctor died but the Sisterhood restored him to life for long enough for only a few minutes, so that he might regenerate into the his next incarnation. (TV: The Night of The Doctor)
Alternative timelines
In a negated timeline Cristophe Zarodnix purchased Karn from the Sisterhood. (AUDIO: Sisters of the Flame)
Behind the scenes
Origins
Karn originated in a theatrical play, Doctor Who and the Daleks in Seven Keys to Doomsday, written by Terrance Dicks. Dicks re-used the name in the script for The Brain of Morbius. The play featured an alternative Fourth Doctor.
This wiki considers neither the play, nor its audio adaptation by Big Finish a valid source and therefore sees The Brain of Morbius as the first appearance of Karn in the DWU.