REM stands for rapid eye movement because our eyes move rapidly during that stage.
Non-REM sleep comes in two variations: the light type of sleep called Stages 1 and 2, and the much deeper version called delta sleep (or Stages 3 and 4).
Going to sleep is like going down an escalator. You start going down into Stage 1, then Stage 2, then into deep sleep in Stages 3 and 4. You then come out of a deep sleep and finish with a period of REM (dreaming sleep). The REM sleep concludes one full cycle of sleep. A full cycle of sleep takes about 90 minutes and there are about 5 or 6 sleep cycles per night.
If you have insomnia don't force sleep, try a light carbohydrate snack, some warm milk or herbal tea. If you continue to experience poor sleep please see a sleep specialist.
Hopefully you have had a good night's sleep. Pack your bags - "Travelling" is up next.