Dolphins sleep by a process called unihemispheric slow-wave sleep. This kind of sleep is believed to help dolphins and other creatures recover from their daily activities.
Dolphins sleep by resting only one side of their brains at a time. When the right side of the brain goes to sleep, the left eye closes. While the right side of the brain is resting, the left side monitors what is going on around the dolphin and tells it when to surface for a breath of fresh air. Eventually, the brain switches sides and the alert side rests. It is estimated that each half of a dolphin's brain gets around four hours of sleep per 24-hour period. This method of sleep developed to allow dolphins to avoid drowning, watch for danger and keep moving to maintain body heat.