What does the Cherokee story make Piper realize?

Piper realizes that her father's life is not as important as saving the world, and that she cannot betray her friends to save her dad. She uses lessons from her mortal side, not her godly side, to decide this. She shows that both sides of her are important in making her the person she is. Her god side might make her a hero, but her Cherokee side has taught her to the right thing.