As far as I can tell..
Imagine if there was a 3D map of the universe; where stars (and planets?) are small dots/spheres. When you activate your hyperdrive, your ship is moved into this 3D map. You get 2 seconds to point in the direction you want; and then your ship races forwards. Where it ends up in the 3D map is where your ship gets teleported to.
Of course the graphics for the "3D map" are probably going to look fancy (e.g. look more like you're speeding through a miniaturised version of space) and have special effects applied. I'd also expect various restrictions; like not being about to exit your ship while its in hyper-space, a time limit so you can't stay in hyper-space for very long, etc.