Dimension

A dimension was a property of space, extending in a given direction, which, when combined with other dimensions of width and height and time, made up the Universe.

Terminology
"Dimension" was sometimes used interchangeably with "parallel universe" or "alternate timeline", but these were different variations of realities.

Dimensions within the universe
N-Space had eleven dimensions. (PROSE: Parasite) Space and time were two of these. They combined into "spacetime."

The First Doctor stated that the "fourth dimension" (as humans understood it) was time. (TV: An Unearthly Child) Vicki Pallister later elaborated that time, even though a dimension in itself, had dimensions of its own. The Doctor even stated, in their adventure at the time, that he did not understand "this" fourth dimension. (TV: The Space Museum)

Hyperspace was another dimension. (TV: The Stones of Blood) It could be reached using a black hole, which essentially collapsed dimensions into a singularity. (TV: The Horns of Nimon)

A TARDIS' interior existed as a separate dimension from the rest of the universe. This meant the interior didn't exist, creating temporal grace. (TV: The Hand of Fear) This may also explain why travel in a TARDIS took "no time at all," as the Third Doctor described. (TV: The Time Monster)

A location of space called the Arc of Infinity was known as an ancient curve between dimensions. (TV: Arc of Infinity)

N-Forms were constructs created by the Patrexes that were able to cross dimensions and exist in pocket dimensions of their own. (PROSE: Damaged Goods)

The Mavora existed in only the first two dimensions, and thus they were a completely flat shape and could slide between the atoms of the universe. (COMIC: The Broken Man)

Other dimensions
There were countless billions of dimensions, some of them incomprehensibly different to N-Space. Beings from these distant dimensions obeyed very different laws of physics and were (presumably) forbidden to cross into other dimensions. Nobody No-One came from a reality 45 billion dimensions away from N-Space and was composed of language and communication instead of matter and energy. (AUDIO: Forty-Five)

E-Space was a small dimension connected to N-Space by the Logopolitans in an effort to delay the death of the universe from entropy. Access was through a Charged Vacuum Emboitment. The Fourth Doctor and Romana stumbled through one such CVE. (TV: Full Circle) They found the Great Vampire hiding there. (TV: State of Decay)

According to Fenric, the Doctor trapped him in the Shadow Dimensions for seventeen centuries (TV: The Curse of Fenric) which were remnants of the Pre-Universe. (PROSE: The Curse of Fenric) The parallel dimension that the Great Old Ones shunted themselves into, which collapsed seconds later into the current universe, may have been one of the Shadow Dimensions. (PROSE: Millennial Rites)

The Seventh Doctor claimed King Arthur's craft found in Lake Vortigern was from another dimension or parallel universe. (TV: Battlefield)

The Antiverse was a universe comprised of Anti-Time. Use of the Oubliette of Eternity would send people to this universe, turning them into Neverpeople. The Eighth Doctor and Romana went there looking for the remains of Rassilon. (AUDIO: Neverland)

The Divergent Universe was a universe created by Rassilon to contain the Divergence -- a race that would theoretically replace the Time Lords. The Eighth Doctor went there on a self-imposed exile. (AUDIO: Zagreus)

Jason Kane spent several years in a hell dimension. It was predominately rock. Tunnelling craft tunnelled their way between habitable areas. (PROSE: The Infernal Nexus)

According to the Tenth Doctor, the Morass was a dimension where time and space had been torn apart. (COMIC: The Crimson Hand)

The bubble universe was a universe outside of N-Space which could be accessed from N-Space via a space-time rift. (TV: The Doctor's Wife)

Species from different dimensions

 * Transcendental Beings, who exist in the higher dimensions such as...
 * The Guardians of Time
 * The Chronovores
 * The Eternals
 * Spillagers (AUDIO: Winter for the Adept)
 * Seven-dimensional Legions (PROSE: Lucifer Rising)
 * Eight-dimensional Scourge (AUDIO: The Shadow of the Scourge)
 * Good Daleks (AUDIO: Project Infinity)
 * Neutron eaters (AUDIO: Lost Souls)