Everyone who has run a race knows that you can break your stride by looking over your shoulder to see how your opponents are doing. Many races have been lost when the leader looked back. When you see that finish line, you are supposed to give it everything you have, because sometimes it is mere inches that separate one runner from another. You must stay focused.
This is the idea behind Paul's statement in Philippians 3:13: "Brethren, I do not count myself to have apprehended; but one thing I do, forgetting those things which are behind and reaching forward to those things which are ahead." Paul was saying, "Don't look back. Don't look behind you."
When God promises, "I, even I, am He who blots out your transgressions for My own sake; and I will not remember your sins" (Isaiah 43:25), He is not predicting a lapse in His memory. God is saying. "I am no longer going to hold your sin against you, because my Son has paid for it at the cross."
Therefore, we need to do what God does: forget our past. We need to learn from our mistakes and remember some of the bitter lessons we have learned. But we no longer need to be controlled by our past.
That is what Paul meant by "forgetting those things which are behind. . . . " Think about the horrible things Paul had done. He was responsible for the death of Stephen and had to carry that in his conscience until his final day. He knew that he was responsible for some terrible things. But he was able to put his past in the past. And we need to do the same.