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REM sleep is a stage of sleep characterized by the rapid and random movement of the eyes. REM stands for rapid eye movement. There are five stages of sleep, the first stage is very light sleep and is where you drift In and out of sleep. Stage two is where eye movement stops and brain wave’s slow, stage three is when SWS starts, slow wave sleep called delta waves that are interspersed with smaller, faster waves.

In stage four there is no eye movement or no muscle activity. Stages three and four are known as deep sleep. Stage five is when you enter REM. Rapid eye movement starts, breathing is irregular, and body parts are temporarily paralyzed.  Heart rate and blood pressure also become irregular. This is where most dreams occur.

REM is what makes dreams more vivid. There are two types of dreams, Hypnagogic and Hypnopompic. Hypnagogic is the experience of the transitional state from wakefulness to sleep Hypnopompic is the state of consciousness leading out of sleep. Floating, falling, flying or spinning, experienced right as we are falling asleep it is called hypnagogic, and when it is right before we wake up it is called hypnopompic.

http://en.wikipedia.org/wiki/Hypnagogia
http://en.wikipedia.org/wiki/Rapid_eye_movement_sleep
http://en.wikipedia.org/wiki/Hypnopompic