Sylvester J. Battley—and who could blame him for preferring a nickname like "Yank" to a name like Sylvester—used to have a reputation in his younger days for being able to break horses. If you think that's a slightly weird, and pretty unfortunate, expression, we're right there with you. But that's not "to break" as in to make something that worked stop working. When it comes to breaking horses, that expression actually means training them so that they can be used to work, on farms and in fields and other stuff like that.
We personally haven't spent a whole lot of time out in the country (we're pretty seriously citified), but back before farming machinery horses were a seriously big deal. And that means that somebody like Yank was, too. In a time and place where a person of color could never count on being respected, you had better believe the kind of respect that he had meant a whole heap to Yank.
Now, thought, all that's changed. The machines have taken over, and nobody needs a guy like Yank anymore. That's what's got him so fed up. "They look at you today and the call you trifling," says Yank, "'cause they see you sitting there all the time not doing nothing. They can't remember when you used to break all the horse and break all the mules" (9.146). Yank feels used, and he's right to feel that way. Yank is Gaines's way of showing us how a broken-down racist system treats people of color as disposable. And when you look at his story that way, it's pretty clear that Yank is more than just an old man who's upset because he's passed his prime. He's yet another example of the way white racism negatively affects people of color.