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—Covey was that dedicated, ruthless, and cunning.
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. We'll hand the mic to Douglass himself to explain what this fight meant:
This battle with Mr. Covey was the turning-point in my career as a slave. It rekindled the few expiring embers of freedom, and revived within me a sense of my own manhood. It recalled the departed self-confidence, and inspired me again with a determination to be free. The gratification afforded by the triumph was a full compensation for whatever else might follow, even death itself. He only can understand the deep satisfaction which I experienced, who has himself repelled by force the bloody arm of slavery. I felt as I never felt before. It was a glorious resurrection, from the tomb of slavery, to the heaven of freedom. My long-crushed spirit rose, cowardice departed, bold defiance took its place; and I now resolved that, however long I might remain a slave in form, the day had passed forever when I could be a slave in fact. I did not hesitate to let it be known of me, that the white man who expected to succeed in whipping, must also succeed in killing me. (10.12)
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).