What does it mean when a cat rolls on its back?

Okay, so over the winter I saw this mangy stray cat wandering by the alley near my building, so coaxed him to follow me upstairs to my apartment. I didn't have cat food or anything since I don't have any other pets, so all I could give him was some water. He stayed for a while and he even let me pet him but after a while he headed back to the door and started pawing at it, so I lead him back downstairs and he went on his way. I didn't see him again after that anywhere in my neighborhood so I figured he was either taken by animal control or dead. But yesterday I happened to spot him in the alley on the other side of the street. I walked over slow because I wasn't sure if it was him, and if it was, if he would remember me. When I approached he did this weird rolling move where he went on his back sorta like how a dog does. I wasn't sure what to do, but I did let him back in my house of course. I was just wondering what it means, like if he was happy. I took at as him showing me that he remembered me, but that's probably not what it really means. Anybody know?