1. A higher dimension of space existing outside of normal space where points in normal space are closer together, thus enabling apparent faster than light travel to be possible. Featured in Star Wars, Babylon 5, the Hitchhiker's Guide to the Galaxy, and the Stargate series, among other science fiction franchises.
Being in the world without earth for a period of time. The area of being below space, not in space, or part of (see MATRIX). Detached or detaching from earth's modern life such as electronics and/or the modern world; Opposite of Hyperspace.
Be like Stephen Hawking and get away from hypospace. Your communicating may be in cyberspace now, but will be attached to hyperspace soon. Detached from cyberspace and the internet, you are definitely in hypospace. That guy looks like he's in hypospace, totally detached from the world.