REM Part is a term used to describe the two parts of the sleep cycle. RAPID EYE Movement (REM) is the part of the sleep cycle when most dreaming occurs, and Non-RAPID EYE Movement (NREM) is the part of the sleep cycle when the body is in a deep sleep. During REM sleep, the brain is active and the eyes move rapidly from side to side. NREM sleep is characterized by slower brain activity and the body is in a state of rest.