To fall asleep unintentionally, especially while seated or in a situation where you should be awake.
"The lecture was so dull that half the class nodded off within the first ten minutes."
I was nodding off in front of the fire.
— A.A. Milne, 'Winnie-the-Pooh' style narrative — widely paraphrased; actual common literary phrasing found in numerous British texts of this period