How do I explain the concept of Teshuvah to my 8-year-old?

Make it small and concrete. Tell her: when we do something wrong, it is like getting mud on our clothes — it does not mean we are bad, it means we need to get clean. Teshuvah is the way back. There are three little steps a child can hold: say "I did it" (no excuses), say "I'm sorry" and mean it, and then do it differently next time when you get the chance.

The last step is the magic one. Tell her that Hashem is not waiting to catch her being bad — He is waiting, like a parent at the door, hoping she comes home. Children understand being welcomed back far better than they understand sin.