Maybe you shouldn't move on. If you don't know why you cheated, and it was stupid and unecessary, then what's stopping you from doing it again? Obviously loving someone isn't a guarantee that you won't cheat on them again, especially since you don't know why you did it in the first place!  Ask yourself this, if presented with the opportunity for a smoking hot piece of not-your-girlfriend ass again, would you take it?  Also keep in mind, that by being given a second chance and not having it held over your head, SUBCONCIOUSLY you may think that it's okay to cheat again.

It really could be just as simple as she's giving you a second chance so just take the damn thing and move on, or it could be more complicated, because you know you've put a dent in your relationship and there are underlying factors to why you can't get yourself over it.  Maybe you're having a hard time moving on because you don't trust yourself to stay faithful, even though you think you love your girlfriend. Or maybe you're wondering how serious your girlfriend is about you, if she doesn't appear to be too concerned about your past indiscretion (you didn't say how hurt she was, only that she gave you a second chance and isn't holding it over your head).

I think you need to have a long, hard sit-down with your inner self and ask some questions.  Do I feel guilty? Why do I feel guilty? In the face of temptation, would I do it again? Can I REALLY see myself staying with my girlfriend and being faithful to her?

Lastly, if you are honestly and truly remorseful about cheating on her, because you know she was hurt and you don't ever want to see the person you love hurt again, then you need to take the second chance that she's given you, forgive yourself, and show her how much you love her by using your words and your actions to help heal the hurt for both of you.