What is Forgiveness?
God's forgiveness is the key act in making us right with God. Each of us has actions and attitudes which get in the way of God's purposes and how God has taught us to be. God pardons these freely, through what is done by Jesus the Christ. Now that we're forgiven, our task is to set others free from our judgement. This by itself does not make the relationship healthy again. But it does clear away your own resentments, your inner stake in the conflict. It's done with clear eyes, working to reduce the opportunity to do the wrong again. You are sowing the seeds for that person's repentance. But it must not be conditional; Jesus calls you to forgive anyway even if they blow you off. You do your part, because Christ did His; they must deal with theirs.
On what was wrong with the sacrificial system, which was still in use in Jesus' day.
Forgiveness is not just a thought or a fleeting emotion. It is a deliberate action. It doesn't happen unless you do or change something. And it is also a decision - you choose to do it. You are led to, sometimes driven to, that action through the power of the Holy Spirit. It can be personal - you forgive yourself and accept God's forgiveness. And it can be between groups. But for most of us most of the time, it is interpersonal, one-on-one. Even then, there is a ripple effect which benefits those beyond just the two.
You can also seek forgiveness in the dictionary. But you'll only find the word; you'll have to turn to God for the actual thing itself.
The Apostles' Creed and the Prayer
When Jesus taught his disciples how to pray using what is known to us as 'the Lord's Prayer', forgiveness was very much a part of it:
"Forgive us our sins,
as we forgive those who sin against us" (BCP, p.364, right column).
The Apostles' Creed is was intended by the early church as a summary of core Christian teachings. In the Third Article, it says:
"I believe in the Holy Spirit;
the holy catholic [universal] Church,
the communion of saints;
the forgiveness of sins,
the resurrection of the body,
and the life everlasting."
The Creed is firstly referring to Christ's forgiveness of everyone's sins. But it means more than just that. The Lord's Prayer says that Christ's freeing us from our sins has a duty that comes with it: we are to forgive the sins of others. It's a core matter of the Christian faith and Christian theology. Neither Jesus (in His prayer) nor the Creed are saying "I believe in punishing others until the life is stomped out of them." They don't say, "I believe in holding on to the sins done against me and mine, forever", or "I believe in my right to really stick it to 'em!". The Creed says, "I believe in... the forgiveness of sins". The Lord's Prayer says, "Forgive us.... as we forgive..." What Jesus did for me, I do for others. Is this for the sake of decency, or public peace? Good reasons, but not good enough for a Christian. Or, perhaps, in order to use the wisdom of religions and sages? That would be good, except that most non-Christian religious or secular-philosophical systems don't give forgiveness the central role Jesus gave it. No. Christians forgive because we're forgiven by Christ, and Christ told us to do the same to others. It is part of the Christian's self-definition.
That said, one of the biggest challenges is to pardon someone who does not forgive others because of the extreme nature of the wrongs. Some things (such as rape, murder, or the Holocaust) bring so much hurt that the person (who is, after all, a human being not God) may simply not find it in them to actually release those who did it. I firmly believe God calls on us to forgive even those sorts of wrongs. That is part of what Jesus meant when He spoke of forgiving 70 times 7 times, and when He said to love your enemies. It's an amazing sign of God's truth and love when someone takes that action. But none of us can stand in judgement about it. We can hope they do it, we can encourage them and teach them to do it and work toward healing that hurt. But we have no standing, under any circumstance, to demand that anyone forgive. That's their own matter before God. God calls on us to do it for even those who find that they can't let go of it. The truth is, no matter how good or strong your faith is, you may find that if you have been done this sort of wrong, you may be the one who's unable to let go. Jesus may then be calling you to forgive yourself for not forgiving, and trust God to heal you.
Jesus Replaces the Temple
In Jesus' day, when you were in need of being forgiven by God, you offered a ritually-clean sacrifice at the Temple, through the official priests in Jerusalem. If you didn't have a ritually-clean animal, you could buy one for a hefty price, and pay for it in Temple currency which, if you had other collateral, could be exchanged for such coins, for a steep fee. People were already getting quite restless about this. They saw the lavish life lived by the keepers of the Temple, and saw how some of them (notably Caiaphas, as archaeologists have discovered) loved the Greco-Roman culture of their conquerors. Even more, as Jews spread out all over the region, they were further from Jerusalem, and thus further from being freed by sacrifices. Yet, it was not the slightest bit less important. More of them were doubting that a dead animal was really what God wanted -- the same doubt their prophets expressed centuries earlier. And there were some who sensed that the Temple could eventually be destroyed if Rome was angry enough over Jewish rebellions. Jesus probably believed that too, and saw it as a justified judgement on what the Temple represented.
When Jesus went to the Temple to overturn the money changers' tables, it was not merely a challenge to the Temple cultus, it was a rejection of the whole Temple system. He had started proclaiming that rejection in Galilee, when he not only healed people, but also pronounced them to be forgiven. But who gave him that authority, they asked? Jesus was, even then, claiming that the Temple system was no longer the place to be pardoned by God. This was now His job, and it could be done anywhere He was. Once he died and returned, he then gave this authority and duty to his gathered followers, through the apostles. So now, wherever people believe in Jesus, there is forgiveness. Even in Jerusalem, even where the Temple once stood.