Parallel universe

As Sergeant Benton once observed, a parallel universe was "some sort of mirror universe, like in that Star Trek episode where Spock had a beard." Amused, called Benton's assessment "succinct". His own belief about parallel universes was more fulsome; to him, a parallel Earth occupied "the same space-time coordinates as this Earth, but in a different dimension. Sideways in time, if you like, rather than forward or back." (PROSE: The Face of the Enemy)

As the Fifth Doctor once explained to Turlough, parallel universes were a specialised form of alternate universe — "alternative universes [that existed] in parallel with each other" — but the terms weren't complete synonyms. A parallel universe had no impact upon another parallel universe; it was "separated only by a millisecond of time and a nanometre of space, without ever having contact". Conversely, a fully alternate universe was when, because of the inherent weakness at the point that one universe split from the other, one timeline actually destroyed the other. (PROSE: Imperial Moon)

At one point, travel between parallels was made simple by the Time Lords, but, according to the Tenth Doctor, travel to parallel universes became impossible after the Last Great Time War. (TV: Rise of the Cybermen)

Examples
In July 1963, the Fifth Doctor visited a parallel universe in which World War II was still being fought. While there he met Gus Goodman, who became his companion. (COMIC: Lunar Lagoon, 4-Dimensional Vistas, The Moderator)

In the 1970s, the Third Doctor visited a parallel universe in which the United Kingdom was a fascist Republic ruled by an alternate Doctor. (TV: Inferno, PROSE: Timewyrm: Revelation)

Circa 1979, the Fourth Doctor visited a universe in which the Roman Empire spanned the galaxy and was beginning to conquer other universes. (COMIC: The Iron Legion)

One parallel universe was lifeless and empty due to the destruction of Logopolis in 1981. (PROSE: The Quantum Archangel)

In the 1990s, Carbury was invaded by knights from a parallel universe which bore similarities to Arthurian legend. (TV: Battlefield)

In 2007, the Tenth Doctor, Rose Tyler and Mickey Smith visited a universe in which Rose's father was still alive. (TV: Rise of the Cybermen)

In 2008, Ianto Jones accepted the offer of Mairwyn. He did not die when the 456 invaded and Mairwyn enslaved Earth. The two later visited the "real" universe to observe Ianto's funeral. (COMIC: Shrouded)

A parallel universe, where Earth was part of a meta-government called the United Federation of Planets, was joined with the Doctor's at one point, resulting in the Fourth Doctor coming in contact with the Federation in the 23rd century and the Eleventh Doctor in the 24th century. (COMIC: Assimilation²)

In one parallel universe, the Ironsides were used to end World War II some years early, then were destroyed. (DWAN: Doctor Who The Official Annual 2011)

Miscellany
Chronovores feasted on parallel universes, but their meals were infrequent because they were banished to Calabi-Yau Space, which provided them no access to the timelines and parallels of the normal universe. once released the Chronovores to normal space, where they threatened to eat away all realities. (PROSE: The Quantum Archangel)

As colloquialism
The term was used sometimes in an inexact way, simply to indicate the unlikelihood of an event. Claudia Bruderbakker once told Peri, for instance, that if her stepmother had been responsible for a particular event, she'd "entered a parallel universe". Peri, familiar with parallel universes, briefly considered the genuine possibility of another universe being created, but then realised that Claudia was speaking figuratively. (PROSE: Synthespians™)