While the exact dates of the story aren't provided, "The Displaced Person" does take place in a specific, and uniquely tragic period in our history – the period generally known as World War II. This time period is most notable for the events of the Holocaust and the bombing of Hiroshima and Nagasaki.
"The Displaced Person" is also historical in the sense of its more immediate setting – somewhere in the Southern United States, probably in the early 1940s. Although some eighty years had passed since the Civil War, the South in particular was still having trouble making the transition out of the slavery. Because the story is framed around both of these historical issues and events, it's historical fiction.
In her essay, "Some Aspects of the Grotesque in Southern Fiction" Flannery O'Connor calls herself a "realist of distances," meaning that she exaggerates the ideas and characters in her stories to get at difficult and mysterious aspects of human existence. She tries to show readers that things that seem far away are closer than we think, and to look at the world from a broader perspective.
Her characters are often presented as grotesque, that is, monstrous on the outside but very human on the inside. Grotesque characters are often feature in Southern Gothic stories. The Southern Gothic is a subset of Gothic fiction. A basic Gothic story uses creepy characters and scary situations to explore anxieties about life, culture, and society. The Southern Gothic story is set in the American South, and often deals with issues of race, religion, and societies still reeling from the effects of slavery and the Civil War.