To browbeat is to intimidate with language. Picture yourself in a police station. The cops are trying to get you to talk by using tough, even abusive, language. They are browbeating you.
When someone browbeats you, they're giving you a beating with their mouth and their mind. If your parents have to browbeat you into cleaning your room, they nag you, yell at you and they may even make fun of you and your bad cleaning habits. While the word brow means forehead, think that they're using their head, or brow, to beat you down. It's a figurative, rather than a literal, beating.