When God forgives our sins, it is saying to forget the sins and
give us another chance. It is not that we forget but we choose to
forget, meaning we choose not to hold it against the person.
For example, if a person has told alot of lies before but you
decide to forgive him. and one day he comes up to you and ask you
to believe him on a matter, you decided to "forget" what he had
done in the past and trust him.
In another words, when you FORGET, you are giving the person a
chance to start all over again AS IF he had done nothing wrong and
NOT that he had done nothing wrong.