What is God's definition of forgiveness?

"I am not able to do that (forgive) myself, not even close. But that is what Jesus would do, and what we should aim for."

I can not forgive of myself either, but I recently read a story about Corrie Ten Boom who harbors Jews away from Nazis during he holocaust, and she later met a Nazi and could not forgive him.

So, she prayed for Jesus to change her heart and enable her to forgive him. She was then able to forgive him from her heart as tears came to her eyes and forgiveness flooded her physical body.

"With man this is impossible, but with God all things are possible."

“And still I stood there with the coldness clutching my heart. But forgiveness is not an emotion—I knew that too. Forgiveness is an act of the will, and the will can function regardless of the temperature of the heart. ‘… Help!’ I prayed silently. ‘I can lift my hand. I can do that much. You supply the feeling.’

“And so woodenly, mechanically, I thrust my hand into the one stretched out to me. And as I did, an incredible thing took place. The current started in my shoulder, raced down my arm, sprang into our joined hands. And then this healing warmth seemed to flood my whole being, bringing tears to my eyes.

“ ‘I forgive you, brother!’ I cried. ‘With all my heart!’

“For a long moment we grasped each other’s hands, the former guard and the former prisoner. I had never known God’s love so intensely, as I did then”

The answer to the question lies in the text "as God has forgiven you". That is, we forgive in the same way He does.

So, how exactly does God forgive us? Does He simply change His anger into something else, or simply cancel the debt? We can with certainty say He does not forgive us by "releasing" something like feelings or debts, or arbitrarily changing something; He forgives us only by executing His Son on the cross, so that He died our deaths.

If we are to forgive each other "as" God forgives us, then we must stop disconnecting this action in our minds from His action on the cross. The "as" shows grammatically that we are to forgive with the exact same means as God forgives. The difference is that when we forgive, we invoke His completed action; we do not declare our own. This is also how Jesus forgave the sins of the paralytic; He invoked the Father's action on the cross that still lay in the future. Now we invoke that same action that lies in the past. For the sins of those who will never be part of God's kingdom, we invoke God's justice to be completed perfectly in the future.

My understanding of it is this:

Both emotions and the will are involved in forgiveness and resentment. We are not fully in control of our emotions (as part of our fallen nature) but we are fully in control of our will.

The exhortation to forgive others ("forgive those who trespass against us") is referring to the will. God will not ask us to do something impossible, like exert full control over our emotions. So you may indeed be guarded with someone who has hurt you in the past. But the question is whether you nurse the resentment or make a conscious effort to forgive.

Matthew 18:21-22 New American Standard

21 Then Peter came and said to Him, “Lord, how often shall my brother sin against me and I forgive him? Up to seven times?” 22 Jesus said to him, “I do not say to you, up to seven times, but up to seventy times seven."

I have heard this interpreted as not only applying to future wrongs the person does, but also to the same wrong over and over. Sometimes we have to make multiple efforts to forgive people because our emotions keep influencing us to resent the person. But Jesus is telling us to be persistent with ourselves.

Forgiveness means not holding ANYTHING at all against them. It's 100%. You wish them the best, you hope they grow to know Jesus. You pray for them because you love them. This in fact is what we are commanded to do to even our worst enemy. The guy who raped and killed your daughter.

I am not able to do that myself, not even close. But that is what Jesus would do, and what we should aim for.

In regards to being "guarded". That is different. Jesus said "don't throw your pearls to the pigs". You got to know who the pigs are to beware of them. But just because you know someone is say, a murderer, doesn't mean you hate them or judge them as closer to hell than you yourself are. Imagine if you visited him in a cell, you might tell him, "brother, you got to stay in here cause you might kill someone". But at the same time your heart goes out to him and you put your arm around his back and pray with him.

This is far from a complete answer to "what is forgiveness", but just to address one portion of your question: I don't think that forgiving someone means that you cannot take steps to protect yourself from further harm. Like if my neighbor robs my house, forgiving him does not mean that I do not lock my doors, or that I trust him with my ATM card and password.

I think forgiveness does mean that I do not punish the guilty person or demand that he be punished, and that I do not repeatedly bring up the offense. Complete forgiveness would mean that you do not demand any penalty at all. A lesser forgiveness would be to accept whatever penalty or compensation has already been taken as sufficient.

For example, suppose your neighbor breaks into your garage and steals your lawnmower. You discover it was him. You confront him and he gives back the lawnmower and apologizes profusely. Forgiveness would be to accept his apology, not press charges, and never bring the matter up again. The greatest forgiveness of all would be to tell him to keep the lawnmower.

Jesus said to be "as wise as serpents, but as gentle as lambs.". Being a Christian does not mean checking our brains at the door when it comes to interacting with the world. Indeed, we are often called to be "discerning."

My interpretation of that word is this - forgiveness doesn't mean forgetfulness.

We can still be guarded when dealing with others, and if they are looking like they are truly changing, give them more trust. When John Mark left Paul, for example, Paul initially said not to trust him. It wasn't until the end of his ministry that Paul changed his mind, mostly on the evidence of a track record.

Forgiveness would imply giving people a chance to make amends - to be different - but it doesn't imply an open invitation for somebody to demand trust that is not warranted by their behavior.