First of all, it is important to understand that the story line of a short story typically revolves around the central problem, also called the "conflict." This means that events in the story are building toward a climax and resolution that (hopefully) solve this problem.
"Desiree's Baby," by Kate Chopin, is a short story that takes place in the Antebellum South. This is the time in America's history between the Revolutionary and Civil Wars. During this time, slavery was both legal, and highly practiced in both the north and the south. Creole Louisiana, the setting of the story, was known for its rich culture of plantation owners, mixture of demographic backgrounds, and high favor of slavery.
The central problem in this story lies in two mysteries that are heightened by the story's historical context. Desiree, the protagonist, is the adopted daughter of wealthy slave owners, and married to a man who has equal social standing. When she and her husband Armand have their first baby, it is slowly revealed that the baby resembles a slave who is one-quarter African. It is determined, therefore, that the baby is part black.
It means…that the child is not white; it means that you are not white.
Socially speaking, this is unacceptable for a rich white couple in the south. Of course, Armand immediately assumes it is Desiree who must have a black slave in her ancestry, because as an adopted child, her history is unknown. The rest of the story chronicles the unfolding events of Armand's assumption, and of course, a surprise ending.