Rapid Eye Movement Sleep (REM Sleep) is also known as paradoxical sleep because REM Sleep brain electrical activity is close to the one observed when awake, while muscle activity is inhibited. During this sleep stage, although they are closed, your eyes move a lot.
We usually think about REM when we talk about dreams because if you were to be woken up during this stage, you would most likely remember a dream quite precisely.
Please note that more and more studies tend to show that we also dream during Non Rapid Eye Movement Sleep (NREM Sleep). Yet, we keep poorer memories of such dreams.
REM occupy approximately 20-25% of your nights but is mostly present at the end of the latter. Consequently, when you are sleep deprived, it is the REM Sleep stage that is reduced. Moreover, if you accumulate sleep debt, deep sleep tends to increase, hence, REM Sleep proportion decreases even more.
Therefore, the duration of REM Sleep can vary from one night to another, or even from one sleep cycle to another.