This woman was caught in adultery and Jesus said this:
LUK 7:47 I tell you, her sins - and they are many - have been forgiven, so she has shown me much love. But a person who is forgiven little shows only little love."
48 Then Jesus said to the woman, "Your sins are forgiven."
49 The men at the table said among themselves, "Who does this man think he is, going around forgiving sins?"
50 And Jesus said to the woman, "Your faith has saved you; go in peace."
Jesus is also showing here that those who sinned a lot in their old life, appreciate Jesus' forgiveness much more than those who sinned just a little (in comparison). And therefore, they love Jesus much more. They see his love for them as much deeper.
He made us perfect forever! He does not remember our sins!
HEB 10:14 because by one sacrifice he has made perfect forever those who are being made holy.
15 The Holy Spirit also testifies to us about this. First he says:
16 "This is the covenant I will make with them after that time, says the Lord. I will put my laws in their hearts, and I will write them on their minds."
17 Then he adds: "Their sins and lawless acts I will remember no more."
18 And where these have been forgiven, there is no longer any sacrifice for sin.
When Jesus died on the cross, we exchanged our "clothes". Jesus took our sin, and we put on Jesus' righteousness on ourselves.
So when God looks at us (IN CHRIST), He sees Jesus. (we are a body of Christ). He sees us clothed in the righteousness of Jesus.
GAL 3:27 for all of you who were baptized into Christ have clothed yourselves with Christ.
1CO 12:27 Now you are the body of Christ, and each one of you is a part of it.
1PE 2:24 He personally carried away our sins in his own body on the cross so we can be dead to sin and live for what is right. You have been healed by his wounds! (healed spiritually, from the decease of sin)
ROM 8:1 So now there is no condemnation for those who belong to Christ Jesus.
Righteousness is given to us by faith, (not by anything we did or did not do).
PHI 3:9 and be found in him, not having a righteousness of my own that comes from the law, but that which is through faith in Christ - the righteousness that comes from God and is by faith.