The initial, or inciting, incident in a story is the plot point that initiates the protagonist's entrance into the story's main action. It often disturbs his or her life in such a way that the conflict begins to emerge and take shape. We learn the initial, or inciting, incident of this particular story within the two sentences:
Knowing that Mrs. Mallard was afflicted with a heart trouble, great care was taken to break to her as gently as possible the news of her husband's death. It was her sister Josephine who told her, in broken sentences; veiled hints that revealed in half concealing.
In other words, Louise Mallard's husband, Brently, is believed to have been killed in a tragic railroad accident, and—due to her apparent weakness of the heart—her friends are very careful to break the news to her in as gentle a manner as possible. It is only after she learns that news that the major conflict of the story begins to become clear, and this is the conflict between Louise Mallard and society. The rules and standards that govern late nineteenth-century society mandate Louise's subjugation to her husband; she has few rights within their marriage, and she did not feel "free" during her husband's life. Only now that she believes him to be dead does she finally feel "free." He was "loving," she knows—not a bad husband at all—but it seems that the institution of marriage is what restricted her, and her husband was really only a representative of society in his expectations of her.