Hyperspace was a dimension distinct from normal space, where one could travel faster than 180,000 miles per second and avoid the time distortion effect stated in Einstein's Theory of Relativity. According to the Fourth Doctor, it was an absurdity — it was only supposed to be a theory. (TV: The Stones of Blood)
Hyperspace was a subset of the Time Vortex, (PROSE: The Crystal Bucephalus) and one account referred to the "vortex" of hyperspace; it may have been the core of the Time Vortex. (PROSE: State of Change).
Hyperspace allowed ships to travel great distances while in another type of space which allowed for an alternative to faster than light drives. The ships would disappear from normal space, enter hyperspace and return. (TV: Nightmare of Eden) Icarons could be used to allow a ship make the transition between normal space and hyperspace. (PROSE: Original Sin)
Hyperspace permitted communication over great distances. Through use of an ionic vibrator, Prentice, her mind in shock from a fall, was able to hear the voice of Zex, even though he was five hundred light-years away. The Master used the same device to send his thoughts into hyperspace and contact Zex. (PROSE: Listen - The Stars) 100th century androids communicated through webwork transmissions via hyperspace. (PROSE: The Crystal Bucephalus)
By 2815 a section of hyperspace was being used as a short-cut for various ships. The Cerberus ship caused a huge traffic jam when it attempted to escape the hyperspace tunnel as it was closing. The ship was eventually found by the authorities later but it was found deserted, leading to it being called the "Mystery of the Cerberus". By 3012, it, along with the prison ship the Montressor which had crashed into it, became a space station called the G-Lock, where the Festival of Death took place. (PROSE: Festival of Death)