How can someone tell your dreaming and why sleep dreaming so important?

An observer can tell when a person is dreaming because the eyes tend to move rapidly during dreams. This movement can be seen when the eyes are closed. To understand how simple this can be, invite a friend to move their eyes around with the eyelids closed. Researchers in sleep labs can also trace the bio-electronic activity of the brain during sleep and dreaming, indicating various stages of sleep.
... Dreams during sleep are vital to physical, emotional and mental health. They are known to relieve stress and maintain emotional balance. From studies performed as far back as the middle of the 20th century, researchers found that volunteer subjects became agitated and distressed when deprived of dreaming.