He does not deal with us according to our sins,
nor repay us according to our iniquities.
God's mercy and grace extend to sinners in His deep love for us. He provides a way for sins to be atoned and for our relationship with Him to prosper. In David's day, God would forgive through the act of obedience whereby a sinner in faith offered a sacrifice as an intervening priest took the life of an animal and offered its blood so that sin could be atoned. Today, God now sees us atoned by the blood of His Son.
For as high as the heavens are above the earth,
so great is his steadfast love toward those who fear him;
What motivates God to be so merciful to us as to provide costly atonement for our sin? It is His faithful love. God saves us because He loves us. It is about His love and not our value. And it was that love that led Jesus to arrive in a stable in Bethlehem to die on a cross outside Jerusalem so that He could empty a grave and have us forever with Him.
as far as the east is from the west,
so far does he remove our transgressions from us.
We never have to doubt the extent of God's love and forgiveness. When He forgives a sin, He removes it from the record. Just as east and west never meet, so our transgressions once forgiven in Christ, are not to be held against us ever again. That is why God is faithful and just to cleanse us from all unrighteousness when we confess our sins to Jesus! That is so liberating. What joy is mine forgiven in Christ!