Forgiveness is a big word, critical to the distinction of Christianity from every other religion (but we’ll get to that point in the end).
There are several analogies to explain what Christ does to our sins but three great descriptor words would be to cover, heal and conceal. But none of that even matters if we don’t recognize the need for Him to cover, heal and conceal our sins. But it’s true that “for all have sinned and fall short of the glory of God” (Rom 3:23).
Simply looking at the raw text of the 10 Commandments, it’s possible for someone to claim to have “kept the Law” and have not sinned. Yet it says in Romans that ALL have sinned. This is explained by Jesus himself in His greatest sermon when He said “You have heard that it was said to those of old, ‘You shall not murder; and whoever murders will be liable to judgment.’ But I say to you that everyone who is angry with his brother will be liable to judgment; whoever insults his brother will be liable to the council; and whoever says, ‘You fool!’ will be liable to the hell of fire.” (Matt 5:21-22)
That is a very high standard that is completely impossible to keep. And that is the point. To be Holy is to be completely without any kind of blemish. It is impossible for us to ever achieve Holiness on our own, apart of Christ. Without Holiness, we cannot be in the company of God. The only way is to achieve Holiness through the blood of Christ.
“If we say we have no sin, we deceive ourselves, and the truth is not in us. If we confess our sins, he is faithful and just to forgive us our sins and to cleanse us from all unrighteousness.” (1 John 1:8-9) Through His death and resurrection, He covers, conceals and heals our sins, so we are made Holy in His name.
Now, what does all this have to do with what makes Christianity unique? Every other religion on the planet presents a list of things you can DO to earn Holiness and you are then saved by some sort of actions on your part. With an ability to earn Holiness on your own, you are in no need of a Savior. However, Christianity teaches “For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast.” (Eph 2:8-9)
Now this does not excuse us from works for the very next sentence in that passage is “For we are his workmanship, created in Christ Jesus for good works,which God prepared beforehand, that we should walk in them.” (Eph 2:10)
“For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord” (Rom 6:23)