Forgive and Forget?

When one forgives another for a crime committed against them, what does this mean? Does it mean that the sinner is absolved and cleansed? But what of justice and repentance? And, the big question: By what right can one dispense forgiveness to begin with? The problem with the crime is that it is, first and foremost, a transgression of G-d's will. Surely then, forgiveness is His domain alone?!