I don't use the word forgiveness at the moment; it reminds me too much of my childhood understanding of it: "I'm sure he didn't mean it", "he'll know better one day", "it was just an accident", just pretend you're OK and carry on the friendship/relationship with the person.
But of course you can't carry on in the same relationship until they repent to you!
My understanding of forgiveness now is 'releasing them from what they morally owe you'. Now they only owe God.
I pray something like this nowadays (very useful I've found for dealing with childhood hurts):
"Lord, what you suffered on the cross is sufficient punishment for what they have done to me; I am satisfied that their sin against me has been paid by you. So, I release them from what they owe me, they now only owe you for what they have done to me."
I think this is what God means when He tells us to forgive people.
