It's a relationship story told from both points of view. It hurts both of them to look at the picture of the other one, so they put them away and out of sight so the reminder is gone and hopefully they can move on with their lives. They both handle things differently and are separated for a long time, but ultimately realize they still have chemistry there or they are no longer heartbroken when they are reunited some time later, hence the line "I found your picture today". They have come to a place where they are comfortable looking at the other person and there is no longer a constant negative reminder by looking at the image of the other person.
This song really hits home with me. My girlfriend of three years and I had just broke up when this song came out. It was so difficult for me to see her picture or anything that reminded me of her. For what seemed like forever, I would find stuff of hers at my place and it brought back all those painful emotions. I was in a really bad place in my life, and I tried to bury my sorrows through destructive means. She was finding comfort with her family, church, and friends; but I became withdrawn from my family and friends, and was lonely and miserable. The actual use of the word "picture" sunk in deep because one of the things of mine that she treasured above any of the jewelry or gifts I gave her was my picture of me taken as an infant. She asked to keep it at her place to remind her of me when I wasn't there. This was the only picture I have of me as a small child because the rest were destroyed, so it was kind of an important keepsake from my childhood. Anyways, I never got it back and we still have not spoken since the breakup. I have no idea where she is or what she is doing, and I still wonder if she has my picture and if she has put it away.