A Connecticut Yankee in King Arthur's Court talks a lot about the class differences in medieval England and, more specifically, how the peasants are nothing more than slaves. Hank even says so outright, in his typically blunt style:
The most of King Arthur's British nation were slaves, pure and simple, and bore that name, and wore the iron collar on their necks; and the rest were slaves in fact, but without the name. (8.3)
It's hard to get more direct than that, right? Plus, sometimes Hank spends whole chapters on this idea, so you know he means it. Twain hated slavery, and some of his earlier works—like The Adventures of Huckleberry Finn—covered it at length. Slavery had been outlawed when Twain wrote A Connecticut Yankee, but black people in America still faced terrible oppression, a reality that probably bugged Twain something fierce. He's quick to point out here that the peasants are slaves in practical terms, that even if they don't call themselves slaves, they live horrible lives with cruel people controlling their every action. Chapter 13 contains an entire paragraph describing how little freedom the so-called freemen actually have—here's just a bit:
They were freemen, but they could not leave the estates of their lord or their bishop without his permission… (13.5)
This is Twain's way of saying, don't be fooled by labels. People in Twain's time lived lives just as harsh and difficult as the peasants in the book, and the fantasy elements of the book allow him to comment on this without taking the heat for making an overtly political statement. He can draw parallels between the Middle Ages and his time, subtly showing readers how little progress has been made in certain respects.
So how does Hank respond to this grave injustice? He plans to change it wholesale, freeing the country of slavery singlehandedly. He starts almost immediately… but in quiet and subtle ways so as not to draw attention to himself. More specifically, his title—Boss—is decided by popular election instead of being given to him by the king. He says he "couldn't have felt really and satisfactorily fine and proud and set-up over any title except one that should come from the nation itself, the only legitimate source" (8.7). Good on you, Hank.
From there, he moves very quietly to shift the people's minds away from slavery. He starts with gentler changes, like getting people to use soap:
These missionaries would gradually, and without creating suspicion or exciting alarm, introduce a rudimentary cleanliness among the nobility, and from them it would work down to the people, if the priests could be kept quiet. This would undermine the Church. I mean would be a step toward that. Next, education—next, freedom—and then she would begin to crumble. (16.2)
Twain constantly emphasizes Hank's need to move in secrecy—to sneak his goals past the public and enemies like the Church—and in doing so, acknowledges the enormity of the task. Change on this scale isn't going to happen overnight, and it won't come without changing people's attitudes first—no small feat in its own right. The king himself needs to be clapped in irons before he understands that slavery is wrong, and the peasants whom Hank hopes to save need to be deprogrammed like pig-herding potato-farming robots. Hank says:
[…] they have served other people so in their day; it being their own turn, now, they were not expecting any better treatment than this. (2.8)
It takes him a long time—seven years to be exact—but Hank eventually brings about the end of slavery. Again, he delivers the good news straight up, letting Twain show us his character as well as his Great-Emancipator-Goes-Medieval accomplishments: "Slavery was dead and gone; all men were equal before the law; taxation had been equalized" (40.2). Unfortunately, Hank loses all his progress in the end when his enemies gang up on him and send him back to his own time. It's tough to change the world, even when you're ten times smarter than everyone in it.