OK, so slavery isn't literally a monster, but bear with us here. As a child, Douglass doesn't know his parents, and he's poorly fed and clothed. But because he doesn't know any other life, he isn't especially dissatisfied. He doesn't even really know that he's a slave; he mostly just does chores around the house. But we are starting to get the sense that bad stuff is coming. Slavery is out there, and like a monster lurking in its cave, we know that sooner or later Douglass is going to have to go out there and do battle with it.
Though Douglass has seen some bad stuff happen to other people, he manages to avoid the worst of it. He's still young, so the overseers mostly leave him alone. He's young and adaptable, so when he's sent away to Baltimore to work for Mr. and Mrs. Auld, he welcomes the change. At first things go pretty well for him there. He learns to read, and when his master tries to put a stop to this, he learns something even more important: the power of literacy. Eventually he makes enough white friends in the street to learn to write, too.
As Douglass gets older, his owners notice that he isn't quite as easygoing or obedient as they would like. And when a slave is labeled a troublemaker, things are going to get real bad, real fast. Douglass is rented out to Mr. Covey, who for six months steadily and mercilessly beats him into submission. Douglass is too exhausted from work to think and too broken by constant whipping to complain or fight back. At this point, it seems like Douglass has been defeated.
This is Douglass at his lowest, in the depths of despair. Covey has basically reduced him to an unthinking animal, and all hope seems lost. One day, when he is looking out across the Chesapeake Bay, his eyes fall on the white sails of ships sailing free. He has a sudden realization, or epiphany: he had resigned himself to being a passive, mindless slave for the rest of his life, but suddenly he is outraged. How dare those ships be free while he is not? Even though he is still a slave in body, he resolves never again to be a slave in mind.
Covey isn't the monster, not really. But he does represent the monster within Douglass, the part of him that accepts being a slave. As long as Douglass lets Covey push him around, he's a slave in more than a legal sense: he's a mental slave.
Once he determines to fight back, however, everything starts to change. He defeats Covey physically, but the real battle is a psychological one. After Douglass refuses to be whipped again, Covey never even tries. He's still a slave in the eyes of the law, but Douglass now knows that it's only a matter of time before he finds his way to freedom. And even though it takes four more years, he does eventually escape to freedom in the North, where he becomes a leader in the movement to abolish slavery and one of the most famous men in the country.