When Sheeran sings he is able to paint a picture in the listeners mind of what he is going through in his relationships and just in his life in general. I know we don't all live the life of a famous pop musician but we still find our own ways to relate to the experiences he writes about.
With this particular line I think that Ed Sheeran is trying to tell his listeners that if you push away the things that have given you pain in the past, it will no longer be relevant and won't bother you. Although it is very difficult to forget the things that cause you so much pain, it will benefit you in the long run.
If you can't forget about the things that cause you pain, try and fix them. It is very difficult to do but you will be a much happier person once you learn to forgive and forget!
Next time you're dwelling on something that has caused you pain in the past, try and move on, there is no point in dwelling on something that had caused you pain in the past. It's over and irrelevant, move on and be happy!