God’s forgiveness of my sin (and your sin) is definitely a clear example of what biblical forgiveness looks like. God does not forgive my sins because He has to or needs to but because He wants to. God has provided a way (Jesus), so He can forgive my sins and redeem me from the curse (death) of them. His forgiveness of my sins is not something that I have earned or that I deserve, and so it will be with those whom I forgive. They will not have to do anything to earn it, they will likely not deserve it, but I must forgive them as God has forgiven me.
God forgives sin because it is part of His nature to be merciful. He forgives the sins of those who have repented of their sins, applied the adequate sacrifice (the blood of Jesus) to their sin and submitted to the Lordship of Jesus. I forgive because I am a bond servant of Christ, and His spirit dwells within me and compels me to be like Him, to show mercy as He shows mercy. And so I must forgive those who trespass against me, against my loved ones.
Rooted and Grounded 