What is the meaning of "square" in the essay?

The work to which I think you're referring is not an essay, but a short story told from the point of view of a white man watching the lynching and public burning of a black man in a public town square. The title of the short work is "A Party Down at the Square." The "square" is the town square, or gathering area, where lynchings were typically held in the South for public viewing.
What is remarkable about this story, which focuses on an action sequence described from the point of view of a white male spectator, is that nearby, an airplane crashes. Inside of the vessel, the crowd finds the dismembered body of a white woman wearing a white dress. This is important because black men in the South were usually lynched for two things—impudence, which could have been anything, really, from not crossing the street when passing a white person on a sidewalk to daring to have a successful business or something else that a white person wanted; the other reason was being accused of having had sexual relations with a white woman. Ellison contrasts the sight of the dead, dismembered white woman, which arouses the shock, horror, and sympathy of the crowd—one white woman "turned . . . almost as black as the nigger"—while people eagerly await the burning of the black man. At the end of the story, the narrator notes how one white woman scratched his face as she, rather literally, clawed her way through the crowd to get a better look at the burning.