Pocket universe

According to the Eleventh Doctor, a pocket universe or pocket dimension was a "distorted echo of our own" universe. He indicated such realities occurred spontaneously but that they "never last[ed] for long". However, there are also examples of artificially created and longer lasting pocket universes. The Doctor also emphatically told Clara that a pocket universe was not a parallel universe. Because of their short lives, pocket universes were highly dangerous to the TARDIS, which could only survive for a few seconds before being inexorably trapped there as the universe collapsed back into the quantum foam. (TV: Hide)

Distinction
While the terms "pocket universe" and "pocket dimension" may have been interchangeable, Albert Marsden commented that he was not trapped in a whole universe, nor a whole planet, explaining that his "pocket dimension"/time loop merely stretched for five miles and ten days before restarting. (AUDIO: Protect and Survive)

Examples
A dangerous species from the Dark Times was closed by other races in a pocket universe called the Ringpull. They were released by the Fifth Doctor and Turlough. (AUDIO: Ringpullworld)

The Galacti-Bank vault utilised dimensional transcendentalism. The contents of the vault were contained in a pocket universe which could only be accessed by using the correct combination, which changed four times per day. (AUDIO: The Selachian Gambit)

The Seventh Doctor trapped two Elder Gods in a pocket dimension that comprised of just five miles of Britain after a nuclear war. (AUDIO: Protect and Survive)

Hila Tacorien was once trapped in a pocket universe, and was only brought back to the normal universe thanks to the work of Emma Grayling, an empathic psychic who was able to, as the Doctor put it, act "like a lantern, shining across the dimensions, guiding her home". This pocket universe contained a large island seemingly floating in space, on which was a misty forest. Time also ran much slower in this pocket universe than in the prime universe, to the point that a matter of seconds in the pocket universe was equivalent to billions of years in the prime universe. (TV: Hide)

The Celestial Toyroom (TV: The Celestial Toymaker) and the Land of Fiction (TV: The Mind Robber) were thought to be pocket universes.

In order to save it from the Daleks, the thirteen incarnations of the Doctor teamed up together to freeze Gallifrey in time and place it in a pocket universe. While they were unsure if they succeeded, an encounter with The Curator indicated to the Eleventh Doctor that this was in fact successful. According to a Time Lord General and the Doctors, the calculations necessary would take several hundred years so the Doctor worked on them for all of his various lives. (TV: The Day of the Doctor)

The Vess kept a weapons factory in a pocket dimension, powered by energy drawn from the Big Bang. (AUDIO: The Light at the End)