Drop Off Meaning

(idiomatic) (transitive) To deliver; to deposit or leave.

Example:   After two glasses of whiskey, Tom soon dropped off in front of the television.
1922, Margery Williams, The Velveteen Rabbit
  And when the Boy dropped off to sleep, the Rabbit would snuggle down close under his little warm chin and dream, with the Boy's hands clasped close round him all night long.
  Can you drop the kids off at school?
  I'll drop off your books when I see you tonight.
To fall.
  The leaves were slowly dropping off the tree.
To lessen or reduce.
  Sales have dropped off in recent months.