Russel Moore’s answer (from Adopted For Life p. 213):
Forgiveness doesn’t mean you feel that what’s been done to you is okay. It doesn’t mean you have warm feelings toward the persons forgiven. It means you relinquish the right to exercise vengeance. You rest in the fact that God’s justice is carried out by God, either at Judgement Day or at the cross.
I think this is modeled in Jesus, as Peter writes,
 When he was reviled, he did not revile in return; when he suffered, he did not threaten, but continued entrusting himself to him who judges justly.  He himself bore our sins in his body on the tree, that we might die to sin and live to righteousness. By his wounds you have been healed.
(1 Peter 2:23-24 ESV)