Here is the complete sentence: If you wake me up during STAGE 3 REM sleep, I could tell you all about any dream that I was having at that time.
During sleep, human brain usually move through five different stages, one of these stage is REM sleep. REM stands for Rapid Eye Movement. The other four phases are described as Non REM sleep. The sleep cycle usually begin with Non REM sleep. Humans usually enter into the realm of REM sleep after about 90 minutes of sleeping. The first stage of REM sleep usually last for ten minutes, the successive stages get longer than this and the last stage can last for about an hour. Most of the dreams that humans have occur during the REM sleep and if one is woken up during this period, he will be able to vividly recall his dreams.