Hyperspace
Hyperspace, also called witchspace, is a dimension through which hyperdrive equipped ships can travel instantaneously from one star system to the other. There are limits to the maximum distance that can be traversed in one jump.
In the Oolite fanfiction, a hyperspace jump leaves behind a temporary blue hypercloud, which can be used to track the target system, and through which additional ships can jump to the same system, not using their own Quirium fuel.
Entry and exit of hyperspace are indicated by an unpleasant feeling, which experienced hyperspace travellers become used to.
Hyperspace travel looks like travelling through a tunnel with characteristic white rings around it.
Legends
It is rumoured that Thargoids are able to navigate inside hyperspace.
Legend has it that the results of a misjump can be disastrous, varying from ending up somewhere in the middle of a sun or interstellar space, to travelling through time, or returning to normal space inside out. A forced misjump is the last resort of the hopeless.
Theories
See Witchspace: possible to exit?, Witchspace Wake & Explanations Wanted