[technobabble]Throughout space, there are lots of bits of dust and junk. that's why they have navigational deflectors.
When you move rapidly towards an object, any light from it will be shifted in frequency. Thus, the radiation from the object of a lower frequncy than visible light will be shifted into visible light, causing it to become visible. Same thing for objects behind you, except it works on frequencies HIGHER than visible light.
So you aren't seeing stars, you are seeing bits of space debris made visible by the speed you are going at. [/technobabble]
In real life, the effect would be much weirder. The same doppler shift would occur, shifting everything into high frequency radition which would actually kill you. But because of relativistic effects, things behind you get twisted out in front of you. In fact, something in front of you would actually appear to be getting further away!