For starters, we want to make it super-, extra-clear that the term "mulatto," like some of the other racist language you'll come across in Gaines's novel, is not okay. It means a person of mixed ancestry, usually somebody with one parent who was white and another who was Black. But it just happens that the word dates back to about the sixteenth century, and is related to the Spanish word "mulo," which is Spanish for "mule," an animal that is a cross between a horse and a donkey. So, in other words, it's a way of describing a mix or blend of DNA that implies that mix is inferior, stupid, and bred for work. In short, it's just not a word that's okay to use—ever.
Gaines, however, wants us to understand that this word is a part of the everyday vocabulary of the South, along with some other offensive words, and that's why he includes it in the novel. The folks out at what is called "Mulatto Place" include Cherry Bello, whom you can find out more about in another part of the "Characters" section, the twins Ding and Bing Lejeune, Jacob Aguillard, and a guy called Clabber ("clabber" is a word for a kind of soured milk).
The fact that they live in a special area near Marshall is also important, because—even though by law one drop of African blood made you Black—folks of mixed ancestry were often set apart and treated differently than Black folks, and sometimes worse if you can even imagine that. By introducing us to these characters, Gaines is trying to give us a picture of how complicated race, and race relations can be, both in and outside of the Black community he shows us.