The Enigma was a race that existed in a different dimension, which had no concepts that the main dimension had. Members of this species had tremendous abilities that they could use to alter the history and reality of N-Space.
During the Last Great Time War, the Dalek Empire broke into the Enigma's realm and took several of them hostage, blackmailing one to wipe out the Time Lords and make Gallifrey a Dalek colony world. After dramatically making itself known in Gallifrey's proximity and proving immune to all Time Lord weaponry, the Enigma began doing so but twice failed to complete the task, instead finding a kinship with Leela's great sadness, using her to speak to the War Doctor and War Ollistra.
Using the Doctor's TARDIS, the Doctor and Ollistra travelled to the Enigma's dimension and attempted to make peace with it before the Dalek Time Strategist arrived and threatened to destroy the Enigma before the Doctor understood that such an act was ultimately a bluff due to the unstable shielding that the Daleks were using to protect themselves from the realm. Ollistra then asked the Enigma to destroy the Daleks instead, before the Doctor requested it remove both the Time Lords and Daleks from history to prevent any possible continuation of the Time War. Though the Enigma considered it, it ultimately decided to return all intruders to N-Space. (AUDIO: The Enigma Dimension)