Forgiveness isn't the same as forgetting. Our life experiences, good and bad, make us the people we are. To forget those experiences would be to lose the value of what those experiences could, and should, have taught us. Forgiveness, for me, is about letting go.
I was in an abusive relationship for a good few years and when it ended I was still very angry, resentful and unhappy. I tried to forgive my abusive ex as I knew the anger and resentment weren't good for me, but I simply couldn't. I felt she didn't deserve my forgiveness.
Instead (and prompted by people who had been where I'd been), I tried hard to forgive myself. I was angry as hell that my ex had treated me the way she had but I realised that I was even more angry with me because I felt I had let her do it. I'd made some spectacular mistakes in believing her lies and in helping her cover up what how she was behaving. It was my anger at my mistakes that was harming me much more than anything about her.
Once I forgave myself for those mistakes, and realised I'd done the best I could with the knowledge and experience I'd had at the time, a lot of that anger and resentment disappeared.
Since then, I still haven't consciously gone out to forgive my ex or forget what happened during our relationship. Instead, what happened back then simply doesn't matter to me any more. I've let go of the resentment about it. What happened, happened. I can't change that fact and to wish otherwise would be a waste of time and emotional energy. I think it's better to invest that time and energy into making sure that I understand the mistakes I made in the past so I can be sure I won't make those same mistakes again.
There's a great line in one of Melody Beattie's books about resentment that goes something like "Holding on to resentment is like swallowing poison and hoping that the other person will drop dead" Letting go of that resentment is a freeing act, and forgiving ourselves is (I think) a very important step in that.