http://www.greensleep.com/Europe/Gre...pe-slaap.asp#6

The REM sleep, also called Rapid Eye Movement sleep or paradoxical sleep, is the sleep that is vital to our mental health. Our body temperature decreases and blood streams to our brains.

During REM sleep, our eyes follow so to speak what we see in our dreams. If we are wakened up or awake in this stage, we can remember what we were dreaming.

Usually, if you remember a dream vividly you woke up during REM, which is a bad thing.