Cowtowning, cowtowing
It is the improper spelling / word for Kowtowing, which means to touch the forehead to the ground while kneeling, as an act of worship, reverence, apology, etc., especially in former Chinese custom. AKA: to kiss someone's ass or to be submissive.
Her boyfriend is a jerk. They broke up because he cheated, but she's already back cowtowning, cowtowing to him trying to get him to take her back.