Hyperspace is a faster-than-light (FTL) method of traveling used in science fiction. It is typically described as an alternative "sub-region" of space co-existing with our own universe which may be entered using an energy field or other device. As seen in most fiction hyperspace is most succinctly described as a "somewhere else" within which the laws of general and special relativity decidedly do not apply – especially with respect to the speed of light being the cosmic speed limit. Entering and exiting said "elsewhere" thus directly enables travel near or faster than the speed of light – almost universally with the aid of extremely advanced technology.
Astronomical distances and the impossibility of faster-than-light travel pose a challenge to most science-fiction authors. They can be dealt with in several ways: accept them as such (hibernation, slow boats, generation ships, time dilation – the crew will perceive the distance as much shorter and thus flight time will be short from their perspective), find a way to move faster than light (warp drive), "fold" space to achieve instantaneous translation (e.g. the Dune universe's Holtzman effect), access some sort of shortcut (wormholes), utilize a closed timelike curve (e.g. Stross' Singularity Sky), or sidestep the problem in an alternate space: hyperspace.
Hyperspace is sometimes used to enable and explain faster-than-light (FTL) travel in science fiction stories where FTL is necessary for interstellar travel or intergalactic travel. Spacecraft able to use hyperspace for FTL travel are sometimes said to have a hyperdrive.
Detailed descriptions of the mechanisms of hyperspace travel are often provided in stories using the plot device, sometimes incorporating some actual physics such as relativity or string theory.