Scientists know about as much about the dreaming brain as they do the waking brain -- in other words, there's still a lot to learn about how the brain creates the dreaming consciousness and wakeful consciousness, said William Dement, leading sleep researcher at Stanford University...
You are conscious in your dreams in basically the same way you are conscious in real life, but you don't remember dreams as well because memory processing is down, Dement said. The continuity of real life experiences helps you distinguish waking life from the dream world. For example, you don't magically reappear in a different setting in the real world, whereas it might appear that way in a single night of dreaming.
"In some ways, it's very good we don't remember our dreams very well," he said. "You'd constantly be saying, 'Did that happen, or was it a dream?' "
For more on the mystery of dreams, check out a Stanford Medicine piece I wrote a few years back.