Hyperspace refers to a parallel realm, outside our own, commonly used to travel through space at great speed from one point of space to another point of space. Hyperspace may also refer to a region of space where other lifeforms exist.
Hyperspace refers to realm in the universe that runs parallel to our own but is accessibility except through scientific means. Commonly Hyperspace is used to assist a ship in Faster Than Light (FTL) travel using a device, commonly called a "Hyperdirve". However the term "hyperspace" may refer to more than just FTL travel such as a place that hosts creatures and other lifeforms.
The earliest literature work using the idea of traveling through space in a secondary realm outside the normal realm is found in "Somnium" (1634). Where Humans travel to the moon with the help of "demons" from another realm.
The term hyperspace was not used to describe this phenomenon till the early 20th century starting with the literary works "Amazing Stories" and "Astounding Fiction". Since then Hyperspace has been a widely popular Sci-Fi term used in various works of literature, film, and even in theoretical sciences.