When a person sins against us, the enemy loves to place within us a wall against that person; a roadblock in our way of loving that person as Christ loved us. Forgiveness is basically a choice that we make to destroy that roadblock that is in our way of loving them as Christ loved us.
Jesus died to tear down the roadblocks caused by our sin between us and God, and we are required to do the same to those who wrong us (Matthew 6:15).