R.E.M Sleep, or, "Rapid Eye Movement" sleep, isn't just accountable of the sequence of dreaming, but is rather the mandatory procedure in which the brain enters a full deep sleep, and full stage of unconsciousness when sleeping. It is mandatory, and can be gained by almost anyone, based on their sleeping patterns, their health, and their methods of getting to sleep.
Most people, in the world, most notoriously North America, do not experience full R.E.M sleep daily, but more of occasionally (three, or five times a week individually. I'm speaking of full R.E.M sleep.) Which is why most people wake up tired, even if they're convinced of getting a good few hours of sleep.
R.E.M is stereotypical for being the factor to how dreams start, theoretically, because your consciousness has subsided into an unconscious state, in which rather the sub-conscious mind begins to "project" random, and rather irrelevant sequences of images, memories, or knowledge. This is dreaming.
The reason why people dream, most likely, is because the sub-conscious mind is what is prone to holding unconscious functionallities in the mind, or being responsible to reacting, or responding, to those without the full consciousness' consent, in which is what you process being aware.
The sub-conscious may be a factor to actually initiating dreams in your sleep, but dreams are also rarely, but possible to be obtained even without full unconsciousness. This is not day dreaming, this may consist of dozing, or gazing, which is pretty much being unconscious while sleeping, but not experiencing an R.E.M sequence, most dreams in these certain sleep categories, usually change by what is happening around you in real life. They can change if you are dozing in a classroom, and the teacher is speaking. Your mind may still be aware of the person speaking, but your sub-consciousness will be synchronizing these processed topics, and changing them into surreal, or logical dreams.
Basically, R.E.M sleep is deep sleep. You experience it every day, but those who still feel sleepy after a good few hours of sleep, may have not experience a fluent R.E.M sequence. In that case, go to bed early, wake up early, keep your patterns up, and in typical healthy advice; eat healthy. (It does equal to efficiency in sleeping.)
i don't know if this is logical, it's pretty much theory. i don't get much R.E.M sleep myself.