How is it possible to forget, even if you really want to?

A very honest person (I know this) said that they had forgotten, totally, had no recollection at all of something bad that had happened in their past. They had wanted desperately to forget about it and had made a pact with someone to forget and then had. When something happened that forced them to remember, at first it was a complete surprise to them and then a shock as the full memory returned. I believe them, because I don't think this person is capable of lying, but how is it possible, that's what I need to know. They don't know, all they can say is, that it was awful, so they made a pact and forgot. They say it took some time, but whenever any thought of this thing had begun, they'd stifled it and thought good things and eventually, it never came to mind any more. I hope you can help me to understand this, it's very important to me, thanks, Hark :)