Generally, forgiveness is a decision to let go of resentment and thoughts of revenge. The act that hurt or offended you might always remain a part of your life, but forgiveness can lessen its grip on you and help you focus on other, more positive parts of your life. Forgiveness can even lead to feelings of understanding, empathy and compassion for the one who hurt you.
Forgiveness doesn't mean that you deny the other person's responsibility for hurting you, and it doesn't minimize or justify the wrong. You can forgive the person without excusing the act. Forgiveness brings a kind of peace that helps you go on with life.