The hyperspace is a notion invented by science fiction authors to free themselves from the limit of the light speed in our universe, which makes the space travels (especially interstellar) very very long.
So the hyperspace is a “parallel space” or “supplemental dimension” in which this limit doesn’t exist anymore. The space travels are then shortened from a factor which depend on the author (no universal rule).
Matching words: Hyper-luminous, Warp