The idea of 'hyperspace', and the word itself, was invented by a science fiction writer back in the 1940s. Just who first used it is the subject of some argument, but by the 1950s, readers were fully aware of the meaning.
Since nothing can travel faster than light, it could take many lifetimes to travel through the vast distances in space. You can see that this would be a problem for our hero, if he had to race to another solar system to right wrongs. So 'hyperspace' was invented. It makes use of travel through another imaginary dimension, in which these distances shrink, so that journeys last only days, or even minutes.
These days, people talk about 'wormholes'. This is much the same thing, where it is suggested that in another dimension two distantly-separated points in the universe become co-incident, and so the travel time between them would be instant. Unlike the imaginary 'hyperspace', 'wormholes' do exist in theory, and some serious people are doing some serious research on them.