I can certainly see how an apology can make it easier, especially if it comes from the other person truly understanding what they did wrong and that the apology is actually heartfelt. I think the person who was hurt has to be convinced the other has truly realized what they did to them. Unfortunately, sometimes that is not possible. For instance some people are coming to terms with what their parents did to them but the parents have passed away. Or sometimes the other person is simply unable to truly understand how they hurt you or the apology made seems superficial.

In my view, the kind of forgiveness that must require an apology is a different kind of forgiveness than the one I stated here. The former is one where you try to continue relating with the person in the exact same way as before, the same bonds, the same vulnerability. We apologize to mend the temporarily broken bond and go back to things as they were. But this kind of forgiveness is different. This one comes with redefining the relationship, and a new understanding. You mentally step back. You protect yourself. Think of an extreme case, a woman forgiving her rapist. She can not do unless she is in a safe place, has processed what just happened, and redefines her relationship to this person (her expectations, beliefs, her feelings, etc). This second kind of forgiveness comes from a place of power and generosity and a new mental and emotional (and sometimes physical) distance filled with compassion. You can not come to it on the first step nor force it. You have to work your way towards it. Once you reach it, you realize you are not forgiving them from the same place you were before when you were victimized and vulnerable. This is a whole new stance.
Yeah there are variations in the definition and this one was referenced a few places so I quoted it and it does make sense to me too. Like yourself, I did not know what it meant and so found reading it and thinking about it helpful.

You're very welcome.