When I was younger, this phrase always perplexed me. I totally got the forgive part. Boom. Done. But I never understood how in the world anyone was supposed to forget an act that was worthy of doling out forgiveness for.
I mean in my book, that's pretty much like showing me a picture of a giant purple elephant and then telling me to not think about anything, especially not the elephant. Ten seconds later, what am I thinking of? The stinking giant elephant that I can't get out of my head.
In my more legalistic, works-based younger years, I viewed sin as this giant purple elephant. Sure maybe God forgave me for my sins, but they were still there (and numerous), staring him in the face, just waiting to be brought up again. The thought that God forgave my sins was never truly comforting because I felt like I had to do lots of good stuff to make up for the sin that God had forgiven me of but never really forgotten.
I couldn't view this cliche phrase through the lens of the Gospel when I was younger, but now I understand two pivotal things:
1) God didn't just reserve his wrath for another day every time I asked him to forgive me for something. He isn't on some sin vendetta to randomly bring up all our sins and throw them in our face when he has had enough. He's a loving, tender father; he's also completely holy. His righteous wrath was completely consumed by Jesus when he sacrificed himself on the cross for my sins. This sacrifice was confirmed when Jesus rose from the dead. My sins aren't sitting on a platter right under God's nose. They're gone!
2) When God looks at me he doesn't see all my crap. He sees Jesus, because Jesus stands in my place before God as my representative. That's why I love Isaiah 61 which says that as believers we have a garment of salvation and a robe of righteousness. These things are not woven together by our own good deeds, but are gifts of grace from what Jesus did on our behalf. Instead of righteous deeds like polluted garments (Is. 64) Jesus wraps us in the salvation he purchased for us and his own righteousness!
So next time you're reminded of your very finite human abilities to "forgive and forget," reflect on God's character - how he truly forgives and forgets our sin, not as a secret vendetta, but as a loving father, which was made possible because of Jesus' perfect life, sacrificial death and powerful resurrection!