Mr. Covey is a poor white farmer with a reputation of being an effective slave-breaker. When farmers have a troublesome slave, they send him to Covey. Covey's method is to work them and whip them until they can barely remember their own names. He spends all his time sneaking around trying to catch his slaves shirking their work, and he's really good at it. Douglass tells us that none of the slaves ever knew where he would pop up next.
The most important turning point in Douglass's life comes when Covey tries to whip him, Douglass refuses to let him, and they fight it out, more or less to a draw. After the fight, Covey shows that the most important thing to him is his reputation as a slave-breaker. Rather than tell anyone else that one of his slaves stood up to him, he keeps it a secret (and lets Douglass get away with it).