The central conflict in Kate Chopin's "The Story of an Hour" is between the main character, Louise Mallard, and society.
The story begins when Louise's sister, Josephine, is attempting to gently break the news of Mr. Mallard's death in a train accident to Louise. "She did not hear the story as many women have heard the same, with a paralyzed inability to accept its significance. She wept at once, with sudden, wild abandonment, in her sister's arms" and then retreats, alone, to her room. From this, we can know that Louise is unlike most women of her society because she did not respond as other women have to this same news.
Though her sister fears that she may be doing herself harm, Louise is actually engaged in much different behavior: she notices
the tops of trees that were all aquiver with the new spring life. The delicious breath of rain was in the air [....]. The notes of a distant song which some one was singing reached her faintly, and countless sparrows were twittering in the eaves. There were patches of blue sky showing here and there through the clouds [...].
Instead of grieving her dead husband, remembering their life together, mourning the death of his love, Louise is, instead, noticing all the signs of life around her. She whispers the words, "free, free, free!" and "did not stop to ask if it were or were not a monstrous joy that held her." We can understand now that Louise is actually happy, not grieving. She's not happy her husband is dead, per se, but she is happy for her acquisition of a freedom she could never have possessed while he was alive.
It is not that she didn't love him. She did...sometimes. And he loved her. "She knew that she would weep again when she saw the kind, tender hands folded in death; the face that had never looked save with love upon her, fixed and gray and dead." There was no conflict between them, and he was not a tyrannical husband. However, "she saw beyond that bitter moment a long procession of years to come that that would belong to her absolutely."
Louise didn't take issue with her husband, in particular, but the institution of marriage in this time period (the 1890s), in general. She was the legal property of her husband, with no rights or legal identity of her own, while he lived. The narrator even tells us that the lines of her face "bespoke repression." Louise could not be her own person. Her purpose, while her husband lived, was to be his wife, to bend her will to his, to compromise. Now, she will be able to follow her own will, to do just as she pleases when she pleases. Readers can see now that the conflict is not between Mr. and Mrs. Mallard, but it is rather between Mrs. Mallard and society, along with all of society's expectations and limitations of a married woman. Mr. Mallard is only a representative of those expectations.