Hyperspace is a block of systems with the B5 style red swirly background.
Each square of a hyperspace system corresponds to one galaxy map square.
So, if you are in System A, and you can see System B marked 4 squares to the right on the galaxy map, but don't have a warppoint to it, you can take a speed 6 destroyer and jump there in one turn:
1) Jump to hyperspace (1 move)
2) Travel four squares right (4 moves)
3) Jump down to normal space (1 move)
There are tides (random movement) in hyperspace, so ships which run out of supply or take damage, will probably never make it home unless the tides randomly pull them directly over a jumpgate. The tides also make it impossible to maintain a blockade in hyperspace. Defense is a challenge