The timing of sleep in humans depends upon a balance between homeostatic sleep propensity, the need for sleep as a function of the amount of time elapsed since the last adequate sleep episode, and circadian rhythms which determine the ideal timing of a correctly structured and restorative sleep episode. The homeostatic pressure to sleep starts growing upon awakening. The circadian signal for wakefulness starts building in the (late) afternoon.
Thus, in many people, there is a dip when the drive for sleep has been building for hours and the drive for wakefulness has not yet started. This is a great time for a nap. The drive for wakefulness intensifies through the evening, making it difficult to get to sleep 2–3 hours before one's usual bedtime when the wake maintenance zone ends.
Just a quick extract on circadian rythm there. We can see that there is a natural dip during the time people take naps. The reason our body goes through all the N-rem stages during normal sleep is because our body has been producing melatonin due to the dim light. Melatonin causes us to go quickly into a dreamless restorative sleep. Since our body knows it has just worked for an entire day, it knows there is a need for deep sleep before REM sleep. The que to start this is a drop in body temperature and increase in melatonin levels.
In the time span of a nap there is little use for deep sleep, also melatonin levels are almost non-existant and our body's temperature is level since we have usually just eaten. These signals tell the brain that it is only having a nap allowing it to go straight to REM since all we want is to sort the mind and not any bodily processes.
I believe it is around 45 mins of nap time before we truly fall into REM sleep, compare this to the nightly time of 80-100 minutes it is quite a bit faster.