Forgiveness in Marshall Rosenberg's view is all about moving on. It means letting go. If you keep on hating the criminal who stole your money or killed your kid, you keep feeding it energy. That energy can be used for other things, and it keeps you from living your own life. It doesn't mean that you should forget that it happened. It doesn't mean that you approve of what the other did. It just means - in his view - that you let go.
Forgetting - as you say - will not work. Well that's what I think. It depends on what has happened of course. If you were called a bad name in school (not systematically mentally beaten down but occasionally called stupid or something), then forgetting is a real option. When your kid is killed, forgetting is not a real option that allows you to move on. Forgiving can be. It will mean a lot of work, especially in saying goodbye to what once was.