To answer this question you need to focus on and analyse the impact of the death of Mr. Mallard on his wife, Mrs. Mallard. After the initial shock of the news, Mrs. Mallard sits in her room and some kind of realisation or epiphany comes to her:
When she abandoned herself a little whispered word escaped her slightly parted lips. She said it over and over under her breath: "free, free, free!"
Although she fears this is a "monstrous joy," she quickly dismisses this idea and we are shown how oppressed and stifled she was as a woman through her marriage in a patriarchal society. It wasn't that her husband beat her or deliberately mistreated her, but her new-found situation makes her realise how much she had not been free:
There would no be one to live for her during those coming years; she would live for herself. There would be no powerful will bending hers in that blind persistence with which men and women believe they have a right to impose a private will upon a fellow-creature.
It is this discovery of freedom on the part of Mrs. Mallard that makes this short story so profound in terms of it being an act of female liberation - Mrs. Mallard comes to see how restrictive marriage is and begins to look forward to her new stage of life where she can "live for herself" without feeling subjected to a patriarchal institution. No wonder, then, that having made this discovery, the sudden return to it should be enough to shock her into death.