The correct answer is (A) To act in a servile manner; to touch the forehead to the ground while kneeling, as an act of worship, reverence, homage, apology, or absolute submission, in former Chinese custom.

Kowtow comes from Mandarin Chinese k'o-t'ou (k'o [knock] + t'ou [head]).

Examples of use:

• Your boss expects you to kowtow to her.
• Under no circumstances will I kowtow to him.