And no longer shall each one teach his neighbor and each his brother, saying, ‘Know the Lord,’ for they shall all know me, from the least of them to the greatest, declares the Lord. For I will forgive their iniquity, and I will remember their sin no more.” (Jeremiah 31:34, ESV)
We've all forgotten things -- sometimes important things: dentist appointments, deadlines at work, or the precise location of our car keys. Sometimes it's something very important such as your wife's first name or day in which you proclaimed your undying love to her at the alter.
Well don't feel too badly, you're in good company (never mind, feel bad about the first name thing). Did you know that God forgets stuff too? Ok, here's where the similarities end. We forget because we're mortal. We have limitations which cause us to come up short at times. God forgets because he chooses to.
When we confess our sin to God, he chooses to forgive us and just like that, it has been stricken from the record. It will never come up again as ammo in an argument. He's not going to rehash it or dangle it over us to stir up feelings of guilt and remorse.
It is gone. It is forgotten. Praise God for that!