fall asleep

Go to sleep; also, cease paying attention. For example, As soon as the lights were dimmed he fell asleep, or His lectures are so dull that I fall asleep. The literal usage, which uses the verb fall in the sense of "succumb," dates from about 1300; the figurative is several centuries newer. Also see asleep at the switch.

The verb has one meaning:

Meaning #1: change from a waking to a sleeping state
  Synonyms: dope off, flake out, drift off, nod off, drop off, doze off, drowse off
  Antonym: wake up (meaning #2)