I understand what it means in a Christian sense. I've known many Christians and am married to one. You don't have to explain. Since I'm not religious I use the world "forgive" in a non-religious sense.
If you go right ahead and testify leaving nothing out, have someone prosecuted to the fullest extent of the law and have them punished, you have not forgiven anything. You can also "forgive" someone and spare them any serious repercussions, while still vowing never to associate with them or let them on your property again. If I "forgave" someone, the latter is what I would do. Otherwise I wouldn't call it forgiveness at all.