What is sleep?
Sleep serves many important brain functions (e.g., clean up of unwanted, toxic substances), and is an active time for brain communication. During sleep, communication patterns cycle, resulting in “sleep stages.” We can measure this communication using polysomnography (PSG), which combines measurements of brain activity, heart rate, breathing, and limb movement to give a sense of an individual's sleep stages.
What is the difference between REM and non-REM sleep?
Stages 1/2 (light sleep) and 3 (deep sleep) are referred to as “NREM,” or non-rapid eye movement, and are associated with increased activity in sleep-related brain regions and decreased communication between frontal regions and the thalamus - an important area for relaying and integrating different kinds of sensory information. NREM stages result in reduced muscle activity, slowed heartrate/breathing, and fluctuating hormone levels.
Stage 1 is the transition from wakefulness to sleep, and is characterized by theta waves (green pepper). Stage 2 is a relatively deeper sleep with background theta waves and bursts of “spindles” (tightly bundled yellow pepper) and “K-complexes” (higher peak of yellow pepper). Deep sleep is important for feeling refreshed in the morning, and is associated with slow delta waves (red pepper), signifying synchronized neuron firing. Research is ongoing to associate where in the brain and how these waves are generated.
Rapid Eye Movement, or REM, sleep is unique in that there is increased arousal (e.g., faster heart rate/breathing), and fast brain waves (orange pepper) that potentially result from increased communication between the thalamus and brain regions associated with memory and emotion. It first occurs ~90 minutes into sleep, and then more frequently towards the end of the night. Dreams can occur during any sleep stage, but are usually more vivid and dramatic during REM.
 Purves, D., Augustine, G. J., Fitzpatrick, D., Hall, W. C., LaMantia, A. S., McNamara, J. O., & White, L. E. (2008). Neuroscience. 4th. Sunderland, Mass.: Sinauer. xvii, 857, 944.