How has Hester changed by the end.

I think that Hester is more self aware. She knows more about her "sin" and punishment as an extension of her community rather than herself. Hester has come to regard Pearl as a sacred gift and her communion with Dimmesdale as pure rather than sinful.

This is a good addition from GradeSaver,

For one thing, she has suddenly become more active in her desires to protect Dimmesdale from Chillingworth. Seeing her husband leeching the life force out of the minister, she seems willing to commit adultery once more, albeit in a different form now, one that involves betraying her husband in order to save her past lover. She is willing to risk punishment again in order to save Dimmesdale's life. At the same time, Hawthorne notes that Hester has begun to lose her impulsive, passionate sensibility and turn more towards thought, logic, and reasoned action. In learning to understand and take responsibility for her feelings, it seems, she has found a maturity which escapes even the most dutiful townspeople.