Rarely have a dream that I can still remember after I wake up. But in my knowledge, all of us actually enter this dream stage when we are asleep. There are few stages of sleep, and dream normally occurs in the stage before and after deep sleep. If the dream occur after deep sleep, then we can easily remember our dream, as we wake up after this stage.
Regarding the connection between dream and real life, I somehow believe that there are a little connection. For example, we normally dream about things, we worried or thought about before we slept. Or sometimes I dream about an old friend, and suddenly he/she contacted me the next day. Not sure about how science describe dreams, but probably have something to do with beta or delta activity which we enter during sleep stage...
Hmmm need a psychiatrist to explain this...