In one way, you're right; forgiving someone who has hurt us doesn't change the past, and it may not even change the other person (although sometimes it does).
But listen, it does change you! Have you ever stopped to think about the damage you've done to yourself because of your failure to forgive? When someone hurts us, all kinds of emotions try to take control of us: anger, hurt, bitterness, resentment, depression, hopelessness–the list is almost endless. We also may want to lash out in violence and revenge, or we may even plot how we can get even with them through malicious gossip or in some other way.
But every one of those hurts you far more than it does the other person. Anger or bitterness, for example, are like an acid, eating away at our minds and hearts–and even affecting us physically. They also hurt our relationships with others; who likes to be around someone who's constantly angry or bitter? The Bible warns us against becoming like someone who "dies in bitterness of soul, never having enjoyed anything good" (Job 21:25).
The first step in forgiving someone is to turn to Christ for the forgiveness we need. Then ask God to help you forgive this person just as He has forgiven you–freely and fully. An unforgiving spirit cannot live in the light of God's love.