Sleep is a state. "I sleep nine hours per day." If one "falls asleep" that is the process of entering sleep. "I fall asleep in front of the television." Hope this helps.

3 steps: 1. be awake 2. fall asleep (=change from being awake to sleeping) 3. sleep sleep = 睡 fall asleep = 睡着

To sleep does not need explanation being such a simple activity. "To fall asleep" means the passage from our mental state of being awake to that of being asleep; sometimes in that precise moment we have the sensation of a sudden fall, as our muscles relax and gravity will change immediately our position in the bed; this sensation depends upon the starting position and how fast is the process. "She fell asleep while reading Andrew's answer" : past tense