http://en.wikipedia.org/wiki/Sleep_paralysis
Basically summed up, it's when you 'wake up' before your REM cycle is complete. The REM state of your sleep is the deepest and often when dreaming occurs, and your brain will actually paralyze your body so that you are unable to act your dreams out. When you 'wake up', you will be conscious that you are awake, but unable to move your limbs or open your eyes. Often you will feel like something is on your chest, choking you, and preventing you from breathing properly. I have experienced this many times and I find the best thing to do is to relax and don't panic, focus on the idea of moving something, usually a finger.
Some people will say they also feel the sensation of being watched, or will hallucinate