as a verb, 'forgive' typically means to cease feeling resentment or to stop blaming someone for a mistake. It can also be used to refer to granting pardon or amnesty.
'forgive' can be used transitively, in which case the object of the verb is typically the person or thing being forgiven, e.g. 'Frederick's parents forgave him for lying'. When used transitively, the verb may involve an assumed objective complement
'His parents forgave him his mistake'.
She can forgive him for forgetting their anniversary.
The governor offered to forgive their debts if they worked in the fields for three months.
To err is human, to forgive divine.
it is sometimes thought that 'forgive' and 'forget' are equivalent; however, 'forgive' means to stop blaming someone whereas 'forget' means to be unable to remember something. Thus, 'forgive and forget' implies that the blameworthy person is no longer thought of, which is not always the case even if there is forgiveness. Additionally, people usually need closure when they are hurt before they can forgive someone.