Hyperspace is used to travel faster than light.
The exact nature of hyperspace is unknown. Through experimentation, it has been determined that gravity wells in realspace are represented in hyperspace as well. However, they are represented by an expansion of hyperspace. For example, a star in realspace has a gravity well, while the same star coexists in hyperspace as a vast volume, magnitudes larger than the star itself in realspace. A singularity, colloquially called a black hole, is a single point in realspace, while it coexists in hyperspace as an infinite volume.
Travelling through Hyperspace
Travelling through hyperspace is a dangerous proposition, as it is not possible to observe realspace from hyperspace. Because of this, hyperspace jumps are carefully calculated before engaging the jump, and such calculations requires processing power exponential to the impact of the gravity well of the jumping ship.
There are a multitude of different types of hyperdrives, and they can be based on vastly different principles. Some might require deflectors, some might generate time dilation, and some require a base speed before jumping. Of course, some hyperdrives are faster than others, but this can be measured in different dimensions: maximum speed, maximum length of a jump, or just power consumption.
It is possible to steer in hyperspace, but this will usually result in horrible accidents upon exiting hyperspace. However, this can be used to intercept another vessel in hyperspace, if one assumes that the other vessel has a safe exit location, and correctly calculated their route.
After a vessel exits hyperspace, it will have no momentum or velocity. Regardless of hyperdrive concept or underlying theories all vessels will exit hyperspace in exactly the same frame of reference. This frame of rerence is also known as the zero-frame, and so called 'absolute velocities' are defined in this frame.
Observing Hyperspace
One of the things making hyperspace travel difficult is the fact that it is not possible to observe realspace from within hyperspace. It is possible to observer hyperspace from within hyperspace, but such observations are difficult, and mostly used for intercepting or keeping formation. It is, however, possible to observe hyperspace phenomena from realspace, allowing the tracking of incoming fleets, convoys or other vessels.