Dreams: These are sequences of images, emotions, and thoughts passing through a sleeping person's mind. Dreams are notable for their hallucinatory imagery, discontinuities, and incongruities.
Consciousness: This is our awareness of ourselves and our environment. In terms of dreams, it's like being an audience member in the cinema of your mind.
REM Sleep: This is rapid eye movement sleep; a recurring sleep stage during which vivid dreams commonly occur. It's like the projector in our analogy - it plays out the 'movie' (dream) for us to watch (experience).