Isaiah 43:25 (NKJV)
I, even I, am He who blots out your transgressions for My own sake; and I will not remember your sins.
This is interesting, we get the idea that God has saved us to benefit us. And indeed an incredible benefit it is. But this verse says that he forgives our sins, not for our sake, but for His! What possible benefit could He get from saving unworthy people like us? He gets glory from it. It demonstrates His unspeakable love.
I love the word "blots out" used here to describe how God removes our sin. I get the picture of something awful that spilled out and God just cleans the whole mess up. Where does the spilled mess of our sin go? He absorbs it into himself. There is the picture of how Jesus took our sins upon himself.
We have learned out to forgive, but as humans we have a difficult time forgetting. See what it says: "I will not remember your sins." Forgetting is one thing, but purposefully not remembering is another thing...a God thing.
Romans 5:8 (NKJV)
But God demonstrates His own love toward us, in that while we were still sinners, Christ died for us.
2 Corinthians 5:21 (NKJV)
For He made Him who knew no sin to be sin for us, that we might become the righteousness of God in Him.