Going to a strict Catholic school is precisely what prevented me from understanding what forgiveness means for many years. Forgiveness, to that parish, was to be given as stingily as possible and with many reminders for years, "I was able to forgive you, so you should do X for me." The concept of forgiveness was associated with Christianity, which I thought was that school, so I rejected the entire concept up until my senior year of high school. Then I has a Jesuit priest as a teacher and he showed me that it is possible to be religious and even a clergyman as well as compassionate, understanding, and open. He and a close friend of mine taught me about forgiveness:
You've probably gotten a wound on your hand or something at some point and had to change the way you did things while it healed. It scabs over eventually and your new patterns become habit. Then you realize, maybe even weeks later, that the wound is completely healed and you can go back to doing what you used to do (which seems foreign, now). There may or may not be a scar, which may or may not fade. That's what forgiveness is and it can take any amount of time or it might never come about at all. It can also be chosen and scheduled like a surgical procedure or physical therapy. And it doesn't come easily and may require an additional healing period.
The final piece these two wise people let me know was that you don't have to actually let the person know you've forgiven z, though it may show through in your behavior if you're still in contact. It's entirely possible to say to someone, "I've forgiven you for what you did, but I still want no contact with you."
There are some people I'll never be able to forgive and some people I won't be able to forgive until they die. There's the whole thing about this time of year being the forgiving season and other such garble...enough holidays have been ruined by these people and now that I'm away from them, I don't want another holiday brought down by thinking about them.