Biblical Hebrew was three verbs relating to the concept of forgiveness.
The word nasa literally means "to lift up". This word is used to refer to the most genuine type of forgiveness, when a weighty feeling of guilt is removed because someone we have hurt is willing to forgive us. In the New Testament, the corresponding Greek word is aphiemi, which literally means "to send forth". (We know this is the corresponding word because the Septuagint often uses aphiemi instead of nasa.)
The word selach means "to pardon". The corresponding Greek word is charizomai. Being pardoned is different than being forgiven for several reasons:
The Hebrew word nakayh has no Greek equivalent. It means being let off "scot-free" without consequences. The story of David and Nathan in Second Samuel 12 has a clear example of someone who was forgiven but still faced consequences. In order to be let off scot-free, a criminal needs to be pardoned by a judge, not forgiven by a victim.
All three of these Hebrew words appear in Numbers 14:17-19, when Moshe reminds God of God's proclamation of Exodus 34:7.
Now please let the power of my lord be great, according as you have spoken, saying, Adonai is slow to anger, and abundant in loving kindness, forgiving iniquity and rebellion, yet by no means letting off scot-free the guilty, visiting the iniquity of the fathers on the children, on the third and on the fourth generation. Pardon, please, the iniquity of this people, according to the greatness of your loving kindness, and as you have forgiven this people from Egypt even until now.
This passage teaches three things.
First, God is merciful and forgives crimes against himself. In fact, he has a habit of doing so.
Second, God does not unjustly pardon the guilty. Sadly, we are all familiar with examples the extreme situation these verses mention: dysfunctional families in which alcoholism, physical abuse, or prejudice cause consequences of sin to be passed along from generation to generation.
Thirdly, when God has forgiven crimes against himself he might pardon those sins. He can then do so justly, for the sin has been forgiven.
A central issue in the gospels is whether Yeshua can forgive sins against God. If he can he must be divine, for someone can only "lift up" or "send forth" a sin against themself.
The gospels contain two accounts of Yeshua forgiving sin before his death and resurrection. Both teach very different lessons.
The first is a story of the paralyzed man who was lowered into a house which Yeshua was visiting (Matthew 9:1-8). Note that in this story we are not told what the paralyzed man's sins were, but they must have been against God because the sins were being divinely punished by paralysis.
Because the man's sins were against God, Yeshua causes an uproar when he claims he can forgave the sins. Only as someone divine could Yeshua forgive sins committed against God. But the man is forgiven, and his paralysis vanishes. So the lesson in this incident is Yeshua's public proclamation of his divinity.
The second story is about a sin with no victim to offer forgiveness. In Luke 7:36-50, Yeshua is approached by a prostitute.
The woman's sin is against God: she is someone under Torah who is disobedient to Torah, thus rebelling against God's law and rule. She knows she needs God to forgive her, but does not know how to seek this forgiveness from God and so she has been suffering.
The woman's sin is also clearly hurting herself. But she is unable to forgive herself until God forgives her.
That this woman is called a "sinner" instead of an "adulterer" shows her clients were Gentiles. (At that time Jewish law would consider prostitution with a Jewish man adultery against the man's future wife.) Her Gentile clients were not committing any crime by Roman law, and as people not under Torah they were seen as blameless before God if following their conscience (Romans 2:14-15) and thus would not be condemned by their Jewish neighbors (at least if unmarried). Her clients are not victims of her crime, and thus they cannot forgive her.
When this woman, who had been suffering because she needing God to forgive her, heard about Yeshua being able to forgive a sin against God she started searching for him. Yeshua offered her the forgiveness she seeks. Now she has relief, and believes God can and will pardon her. So the lesson in this incident is Yeshua's willingness to help people find peace with God.
What about sins that are not only against God? If their victims will not forgive the sin, can God forgive or pardon those sins?
Before answering this question we must note something about how the nasa kind of forgiveness works. If a crime hurts more than one person then not every victim needs to extend forgiveness. Usually a person seeking forgiveness can feel forgiven even if only one victim forgives the sin, because this is enough to be a convincing statement that someone really does know their sin and still thinks they are deserving of forgiveness.
Before Yeshua's death, the answer was "yes" if the crime was volation of a commandment. In Numbers 5:7-8 and Leviticus 5:17-19 we read the details: the criminal must pay back the victim (full restitution plus one-fifth) and then do the proper Tabernacle offering. Then God, as one of the injured parties because his commandment was violated, would forgive (and pardon) the criminal. The forgiveness would happen whether or not the human victim forgave.
The Tenach never shows God forgiving or pardoning an act that was not a volation of a commandment. For example, if someone was angry and shouted insults, that person could seek forgiveness from those he hurt but could not appeal to God for forgiveness.
Yeshua, after his death, could forgive any sin. Romans 3:25-26 explains that Yeshua was hurt by every sin ever in his death. We are not told how this worked, just that God worked a sadistic miracle. But since every sin has caused hum hurt, Yeshua can now genuinely forgive any sin. This, in turn, allows God to be righteous while pardoning any sin. (To be even more clear about this dynamic, it will be Yeshua will also do the pardoning, according to Romans 2:16.)
So after his death and resurrection, Yeshua can forgive and pardon any sin. This is fundamental to God's offering salvation to the Gentiles, who are not under Torah and thus do not have their sins count as rebellion against God's law and rule.
Yeshua, at his first coming, dealt with the divine ability to forgive and pardon. He did not try to eliminate sin in general.
John 1:29 is usually translated wrong, to devastating effect. Yochanan did not proclaim, "Behold the Lamb of God, who takes away the sin of the world!" Instead, Yochanan proclaimed, "Behold the Lamb of God, who takes away the sins of the world!"
Sin as a concept exists outside of us. It is something we can be a slave to.
When we speak of "our sin" we really mean "our disobedience" or "our crimes" or "our offenses against Adonai". Saying "our sin" is scriptural language, but very sloppy language.
Yeshua did not come to take away sin (singular) from the world. It is our offenses that Yeshua came to deal with. All of our sins are now against Yeshua, and thus can be forgiven by him and justly pardoned by him. God will not take sin (singular) from the world until the time of Yeshua's second coming.
The fact that sin still exists, and that some unsaved people are still enslaved to it, does not affect our salvation. We are not doomed to death because sin exists. Only when a person allows sin to use him or her is that person considered unrighteous. As scripture says "The wages of sin are death" (Romans 6:23), not "sin is death".
Earlier in Romans 6, Paul explains this quite carefully: by law we were a slave to sin and instrument of disobedience earning death, but by grace we are a slave to God and instrument of obedience earning life.
Some people need forgiveness not for any specific sin but just from how they have condemned themselves. Sadly, we have also all known people who have convinced themselves that they are not worthy or love or joy because they believe themselves to be incurable in some way: too stupid, ugly, selfish, lustful, etc.
To these people, Yeshua offers a truth he taught in John 9:39-41: understanding how sinful we are is unnecessary and counterproductive.
Yeshua said, "I came into this world for judgment, that those who don't see may see; and that those who see may become blind."
Those of the Pharisees who were with him heard these things, and said to him, "Are we also blind?"
Yeshua said to them, "If you were blind, you would have no sin; but now you say, 'We see.' Therefore your sin remains.
This is a paradox. If we claim to recognize all our sins, and thus perhaps have dealt with them all (as the Pharisees could through the Temple sacrifices), this pride counts as more sin. But if we realize we do not recognize all our sins, and thus some are not dealt with, then Adonai more easily forgives and pardons these sins of which we are unaware.
Yet this paradox is not surprising. We can all imagine someone who mistakenly believes they have plumbed the depths of their heart and identified all their sins, and how terribly self-righteous and unsocial such a person would be. We can even remember times when we took the forgiveness and pardon Yeshua offers us for granted, and how that tarnished us.
Similarly, there must be near-countless times in the past in which we hurt people and either did not know it or do not remember it. For Yeshua to make us innocent we do not need to revisit each of these sins. In fact, if we have matured beyond repeating those sins it might be better if we don't deal with the past and thus focus more on Adonai and less on ourselves.
In other words, we should recognize all our sin, but the proper way to do this is not to try to see all our sin but to accept forgiveness for our sin whether or not we see it.
This truth holds whether or not our problem is actually sin (selfishness, lust, etc.) or some other source of self-condemnation (intelligence, looks, etc.). Focusing on it only makes it worse. Lifting our eyes from ourselves to Adonai allows healing to happen.
Notice that Yeshua is vital to this reality. Without understanding Yeshua, people cannot properly understand how they can still struggle with sin and still be worthy of heaven. This is why people become more guilty if they have heard the gospel but reject Yeshua's offer of forgiveness (John 15:22).
In John 20:21-23, the risen Yeshua tells his disciples they can forgive sin. What does this mean?
Yeshua therefore said to them again, "Peace be to you. As the Father has sent me, even so I send you." When he had said this, he breathed on them, and said to them, "Receive the Holy Spirit! Whoever's sins you forgive, they are forgiven them. Whoever's sins you retain, they have been retained."
This is not a comforting passage. Yeshua is telling his followers that just as he was sent to suffer, so he could better forgive, we should suffer and be forgiving.
Doing this work is not necessary for anyone's salvation. Yeshua can already forgive any sinner because of his own suffering. And since Yeshua is divine (not us) it is Yeshua (not us) who can pardon sin and bestow God's grace and the Holy Spirit.
But there are many people who need the concrete experience of a person forgiving them. Like the prostitute in Luke 7:36-50, they are suffering under the weight of their sin until someone who knows their sin and has been hurt and disgusted by it is able to look them in the eye and say, "Your sin is forgivable. I forgive you even though your sin hurt me. You are forgiven, and God can pardon you justly."
Furthermore, because we have the Holy Spirit within us, in some small way sin that hurts us also hurts God. This allows us to also say to that person who needs very explicit forgiveness, "Not only is your sin forgivable, and I now forgive you even though you hurt me, but that sin hurt God and he has asked me to say he forgives you too."
Yeshua has sent us to tell that to people. This is why Yeshua so often taught us to not care about physical possessions or honor--we should have our defenses down and expect to get hurt. That's part of our job.
This is what scripture means when it calls to "deny ourselves" and "take up our cross" (Luke 9:23), to "suffer with Messiah" (Romans 8:17) and "suffer on his behalf" (Philippians 1:29), to let "the suffering of Messiah abound in us" (Second Corinthians 1:5) that we may in "fellowship of his sufferings be conformed to his death" (Philippians 3:10).
When we who are Messiah's Body, God's elect, are actively forgiving those who harm us then those people will understand how God can justly pardon them. Otherwise Yeshua's offer of salvation seems absurd, as if God wants to white-wash sins and pretend that people are more innocent that they really are.
Often people pass wickedness around like a game of Hot Potato. Imagine, for example, someone saying something mean to you, putting you in a bad mood so you snap at someone else; then that other person is bothered and drives rudely, cutting off another driver who is made angry; he then speaks sharply to his wife when he arrives at home; and so forth...
Yeshua died to provide the ultimate end to this behavior. His followers, through forgiving other people can bring the wickedness put into their lives to him. Then, at his cross, that wickedness is judged and destroyed.
We "suffer with Messiah" when we repay evil with good, forgiving others and actively bringing the wickedness they produce to Yeshua to take it out of circulation.
Any person trying to be good can do this a little. People of noble intent and a forgiving nature can hold on to some wickedness, not passing it along when they are hurt by another. But it takes knowing Yeshua, having God's Spirit, and being saved from slavery to sin to be able to do this every time.
M. Scott Peck writes about this dynamic in People of the Lie:
I cannot be any more specific about the methodology of love than to quote these words of an old priest who spent many years in the battle: "There are dozens of ways to deal with evil and several ways to conquer it. All of them are facets of the truth that the only ultimate way to conquer evil is to let it be smothered within a willing, living human being. When it is absorbed there like blood in a sponge or a spear into one's heart, it loses its power and goes no further."
Eventually, God will say, "Enough!" and there will be a Day of Judgement. But God's wrath is directed an wickedness, not the people that carry it (Romans 1:18). He would prefer sin to be taken out of circulation than punished on that last day.
Remember not to be frustrated by the fact that you still struggle with sin. Nothing about God's plan for your life is incomplete or broken, for scripture nowhere promises that you will not struggle, and God has not yet tried to remove sin from the world. Persevere, as scripture frequently encourages you to do.
Do not focus on your sin, but focus on God, who continues to conform you to the image of his Son. We are asked to participate in how Adonai makes us innocent, but much still happens outside of our awareness.
Do not be frustrated when people hurt you. Forgive them, and tell them you forgive them, and tell them God is willing and just to pardon this forgiven sin.
If you feel the weight of something you have done but not received forgiveness for, then get that forgiveness. If there is no person willing to extend forgiveness, pray that the Holy Spirit, who teaches us all things, will teach you how that sin hurt Adonai and yet he forgives it. Then you can have peace receiving pardon from God.