The theme of Mulatto is what W. E. B. DuBois called the "color line," the line that separates Black people from white people in a way that "others" Black people as different and less worthy of respect than whites.
In the play, a white Georgian plantation owner in the 1930s named Colonel Norwood has had four children with his Black housekeeper Cora. Because of racism, he does not want to acknowledge these "mulatto," or mixed-race, children as his own, as that would mean they might be allowed to cross the color line and get out their "proper" (subservient) place in the strict Southern social hierarchy.
However, Norwood's youngest son, Robert, who looks much like his father, insists on acting as if he is the Colonel's son—as if he is a white son—no matter how much this annoys his father. For example, as the play opens, the Colonel becomes angered because Robert has taken the Ford out for a drive without permission, something a white son would maybe be allowed to get away with. But to the colonel, for his mixed-race son to do this is an outrage. He says that Robert has to work in the cotton fields like the rest of the Black hands. He calls Robert "yellow," showing that he defines him primarily in racial terms, and refers to him as Cora's son, not his own. Later, after Robert kills the Colonel and realizes he is going to be lynched, he kills himself.
Today, while the issue might be less overt, Black people who cross the color line still risk white reprisal and, as in the case of someone like President Barack Obama, who is also of mixed race, are held to higher standards of speech and behavior than white people in similar positions. And while we no longer have lynchings, per se, Black people in this country are more likely, percentage wise, to be killed by police for posing a threat than are white people. The color line is still an important and divisive issue in our country, even if the situation is different than it was in the South in the 1930s.