Hyperspace is a region in which its co-ordinates correspond to co-ordinates in the universe. However, they are a million times closer together than in real space, so a ship at constant travelling between two points will move a million times as fast through hyperspace than through real space. Electromagnetic radiation will also travel a million times faster.
A spaceship's velocity relative to the cosmic background is retained when they enter hyperspace, though reduced by a factor of a million. It is then increased again upon exit.
Matter does not naturally remain in hyperspace- unless kept there by a Hyperdrive, it will fall back into real space instantaneously. Photons do not drop back down unless within the hull of a ship dropping down.
Objects from real space cannot be detected in hyperspace and vice versa unless semi-hyperspace devices are used.
Looking out from a ship into hyperspace, it appears as a black void, containing no objects other than those with hyperdrives.
Hyperspaces, in turn, have shadow universes called Ultraspaces.