Real Dictionary

forgive
passive verb: If you say that someone could be forgiven for doing something, you mean that they were wrong or mistaken, but not seriously, because many people would have done the same thing in those circumstances.
verb: Forgive is used in polite expressions and apologies like 'forgive me' and 'forgive my ignorance' when you are saying or doing something that might seem rude, silly, or complicated.
verb: If an organization such as a bank forgives someone's debt, they agree not to ask for that money to be repaid.
verb: If you forgive someone who has done something bad or wrong, you stop being angry with them and no longer want to punish them.

forgive in American English
to give up resentment against or the desire to punish; stop being angry with; pardon
to show forgiveness; be inclined to forgive
intransitive verb: to pardon an offense or an offender
transitive verb: to grant pardon for or remission of (an offense, debt, etc.); absolve

forgive in British English
verb: to cease to blame or hold resentment against (someone or something)