In general, here is what happens in the story: Desiree's mother comes to visit Desiree when her...
What might be confusing to you about the story "Desiree's Baby" is that author Kate Chopin deliberately created many ambiguities within the story. That is, she raises possibilities without answering them for reader.
In general, here is what happens in the story: Desiree's mother comes to visit Desiree when her baby is about a month old. The mother is surprised at the appearance of the baby, but Desiree is so in love with the child that she does not pick up on her mother's concerns. Desiree says that Armand is very pleased and happy and that he has even stopped beating the slaves since the child was born.
When the baby is about three months old, however, things change radically. Armand stays away from Desiree and the baby without telling her why. Neighbors from far away come to visit, and Desiree is not told why. Finally as Desiree is observing the child of one of the slaves, she begins to look from the little boy to her baby and something dawns on her. She goes to Armand and asks him what it means. He tells her, "It means that the child is not white. It means that you are not white." Evidently the child has facial characteristics that are typical of blacks.
Desiree objects, saying her skin is whiter than Armand's. Desiree's mother writes to her and tells her she is welcome to bring the baby and come back to live with her. Desiree asks Armand if he wants her to go, and he says he does. Without taking anything with her, Desiree takes the baby and walks not toward her mother's house, but into the bayou, where she presumably would have died with her child. Weeks later Armand has a bonfire to burn all the clothing and accessories of Desiree and the baby. He burns letters he received from Desiree during their courtship. Among those letters he finds a note from his own mother to his father revealing the fact that she is of mixed blood, and some of her ancestors were black.
The story implies without directly stating it that Armand is extremely racist. In the South if a person had even 1/8 black heritage, he or she was considered black, not white. That meant that laws that discriminated against blacks would apply to that person, even if he or she did not look black at all. As a plantation owner, Armand was obviously heavily invested in the social structure of the South and believed that blacks were an inferior race. Desiree was adopted by her family, and when Armand married her, he was wildly in love with her and never considered the possibility she was not completely white, especially since she was very light skinned--at least compared to him.
At first when the child was born, his features did not look African. It takes babies a while to develop their own appearance. Still, at the age of one month, Desiree's mother noticed the features and was surprised. This foreshadows Armand's reaction. When the baby was three months old, Armand suspected the baby was part black, and since he supposedly knew his own heritage but Desiree's birth parents were unknown, he believed he was married to a black woman and had a black child. This was mortifying to him because it would harm his status in his community. The far-off neighbors were probably important members of society who Armand consulted with about the problem. They must have advised him to not accept Desiree or the baby and to get rid of them if he could. Armand treats Desiree coldly, forcing her to bring the matter up. He then tells her she is black. She then offers to leave, certainly hoping he will tell her to stay. But he doesn't. She sees no future for herself and her child without the protection of Armand and "knowing" they will be social outcasts now. So she decides to kill herself and the baby.
In a masterful twist ending, Chopin has Armand find out that he is the one who is of mixed racial ancestry. His mother was part black; she had only lived in France and had never subjected herself to the racial prejudice that ruled the Southern U.S. We assume Armand never knew that about his mother. One of the big ambiguities of the story is how Armand feels now that he knows he is part black. Does he still hate blacks, and does he hate himself? Will he regret having sent his innocent wife and child away to their deaths? Or will he simply burn the letter and go on pretending to be 100% white?
At any rate, the irony of the story is that Armand, who despises the black race so much and thinks it is so inferior to the white race, finds out that he himself is part of that "curse." To comprehend the story, you need to understand the social status of blacks and whites in the South when this story takes place. I hope this explanation helps you understand the story better!