Most Helpful Girl
Everyone has different definitions of what cheating is...
Her begging to take you back does not necessarily imply she cheated in her eyes. She just realizes you're angry/upset with her and therefor wants you back and is willing to make the same mistake again. Of course it really depends on what you view as cheating or not. It's best to talk about these things with your partner in advance so everyone knows what's off limits.
Most Helpful Guy
It means that she understands you have declared a boundary and she does not want to upset you. Now she understands and wants to conform to your boundary as long as it is not too controlling.
It does not mean anything else.
Now the ball is in your court and you can behave like an ass or behave like a man.
We all have to learn how or what behavior is acceptable, but dumping everyone on a misunderstanding leaves us all a little lonely. Give her the opportunity to be a great girlfriend.