Rapid Eye Movement

REM (Rapid-Eye Movement) is a vital sleep stage, and is most well-known for having more frequent occurrences of dreaming. On average, people need 90-120 minutes of REM daily. Unlike SWS, once one meets their REM need, their sleep stages will still cycle between light sleep and REM as long as they continue sleeping.
REM is responsible for storage of procedural memory, i.e. remembering how to do certain things by following a procedure. For example: how to walk, how to ride a bike, how to play a specific piano piece. REM is also responsible for emotionally related memory consolidation, and for spatial memory consolidation (together with light-sleep), i.e. which way to walk to your friend's house.

REM pressure feels like (strong) mental exhaustion and is responsible for most "typical" symptoms of sleep deprivation, e.g. loss of concentration, irritability, etc.

When napping during REM peak, lots of dreams and very deep sleep are expected, resulting in a nap that feels much longer than it is and has extremely restorative effects. Naps are usually a little bit hard to wake from but sleep inertia is relatively low: It takes only a few minutes to become fully functional again even on bad days, usually.

A second "smaller" REM peak exists around noon or early afternoon for many people, and may be similarly worthwhile to nap in than the first. Waking is much easier, but restoration is still very high.