to stop feeling angry with somebody who has done something to harm, annoy or upset you; to stop feeling angry with yourself

used to say in a polite way that you are sorry if what you are doing or saying seems rude or silly

Forgive me, but I don't see that any of this concerns me.

Forgive me for interrupting, but I really don't agree with that.

Forgive my ignorance, but what exactly does the company do?

(formal)Forgive my interrupting but I really don't agree with that.

to say that somebody does not need to pay back money that they have borrowed

The government has agreed to forgive a large part of the debt.

LEARNit Dictionary