He who covers transgression seeks love, but he who repeats a matter separates friends. - Proverbs 17:9
Dwelling on transgression, even in the smallest of thoughts, generates bitterness. Bitterness is such a crippling feeling - it can break one's already established routine simply because he or she remembers being harmed. It can leave one with such a deep empty sort of pain that lingers even after the heaviest of vice-bingeing, only to be amplified accompanying a hangover. Some people believe that if held long enough, bitterness can very well manifest in the physical as sickness. All this comes simply because there exists the temptation to hold on to the pain while the people who hurt us may very well have been way ahead in their own lives.
When you love those who have harmed you, you have overcome them. It's not a one-time deal. There is a reason why Jesus said we should forgive seventy times seven times - it's because while we are in this life, the temptation to repeat transgression is always present, even in the hardest of lessons.
Forgiveness releases both the transgressor and the one who was transgressed. As Jesus Christ has released us from condemnation and any obligation to sin, so we are to forgive, praying for those who have wronged us. We do this for them to see for themselves how we forgive as Christ forgives us. It's not about how we make them feel more than how we totally relinquish them of any obligation for our satisfaction.
By forgiving we demonstrate how we have been forgiven. We pass on the grace which has been handed to us by Jesus Christ.
Forgiveness is easier said than done, but better done than said.