Final answer:
Dreaming occurs during the REM sleep period, where brain waves resemble those during wakefulness.
Step-by-step explanation:
The period in which dreaming occurs is during Rapid Eye Movement (REM) sleep, which is characterized by darting movements of the eyes under closed eyelids. Brain waves during REM sleep appear very similar to those during wakefulness. Non-REM (NREM) sleep is subdivided into three stages distinguished from each other and wakefulness by characteristic patterns of brain waves. REM sleep typically follows these stages. Dreaming is thought to represent life events that are important to the dreamer or even a state of proto-consciousness, constructing a virtual reality that may help in wakefulness.