Forgiveness is something that we all have within us, but we don't always choose to use it. Sometimes people hurt us and forgiving them just doesn't seem like the right decision at that time. In the end we always end up forgiving the person even if they don't deserve it or even if we weren't quite ready to give them that forgiveness.
Why do we do this? We do this because no matter how bad someone hurts us, we are all human. It hurt when they did you wrong, that shows that you care. The fact that we care is what pushes us to forgive them in the end. Sometimes we just don't want that person to feel as bad as we do, so giving them forgiveness makes us feel like maybe we helped them move on and feel better about the situation.
Just remember that they did hurt you in the beginning, try not to let them off the hook right away.