What is forgiveness, specifically? When someone has wronged you, it means they owe you, they have a debt with you. Forgiveness is to absorb the cost of the debt yourself. You pay the price yourself, and you refuse to exact the price out of the person in any way. Forgiveness is to a) free the person from penalty for a sin by b) paying the price yourself.
The ultimate example. We are told that our forgiveness must imitate God’s forgiveness in Christ. Be kind and compassionate to one another, forgiving each other, just as in Christ God forgave you (Eph.4:32). a) How did God forgive? We are told that he does not ‘remember’ them. That cannot mean that God literally forgets what has happened–it means he ‘sends away’ the penalty for them. He does not bring the incidents to mind, and does not let them affect the way he deals with us. b) How did God forgive ‘in Christ’? We are told that Jesus pays the price for the sins. ‘It is finished’ means ‘It has been paid in full’ (John 19:30). The Father gave up his Son, and the Son gave up his life. God absorbed the cost in himself.

-Tim Keller