The central issue of "The Story of an Hour" is the emergence of a woman feeling freedom and independence, perhaps for the first time in her adult life. As the story begins, Louise Mallard learns of her husband's death. She immediately weeps uncontrollably and then retires to her room alone. After sobbing and calming down a bit, she begin to have an "awakening" (to quote another of Chopin's titles).
She could see in the open square before her house the tops of trees that were all aquiver with the new spring life.
The narrator continues describing vibrant images and events that Louise is witnessing. This next line expresses Louise's transition or metamorphosis from dependent wife to free woman:
She was young, with a fair, calm face, whose lines bespoke repression and even a certain strength.
Louise had been repressed in her marriage to Brently. This is not to say that he was a bad husband. But Louise had felt pressured to perform the duties of a loyal wife. She felt trapped in this old fashioned role and felt trapped in being dependent on her husband. And note that the story was written in 1891 when women were much more oppressed by their husbands and society in general. (For instance, at this time, women could not yet vote.) When Louise gets over her initial grief, that inherent strength begins to surface and she is filled with the joy of freedom. When Brently returns, her roller coaster of emotions ranging from grief to absolute joy to complete shock is too much for her heart. And although the last line indicates that the doctors determined she died of "joy that kills," she may have died from a disappointment that kills.
The initial conflict in the story is Brently's supposed death. The subsequent resolution would be the family dealing with it. But the actual conflict in the story is a much broader social issue. The conflict is the inequality of the two genders. In other words, the conflict has to do with the historical oppression of women. Even in this story, where there is no indication of a bad marriage, Louise has always felt trapped and oppressed, forced into a role she did not want or maybe even choose. Perhaps she wanted to work but Brently would not allow it or the society they lived in was just too traditional and she felt compelled to be a housewife. In any case, she felt trapped. This conflict is resolved momentarily with her brief experience of freedom. This conflict is reintroduced when Brently returns, and with her death, it remains unresolved; just as the struggle (especially in 1891) for women's rights had remained unresolved.