What is it that really kills Mrs. Mallard?
Mrs. Mallard has a weak heart, and upon hearing that her husband is not dead, and that is not free from the confines of her marriage as she had thought, that is when, ironically, her heart gives out and she dies of shock.
To add to what the above poster said, it is ironic that Mrs. Mallard dies, not because of news of her husband's death, but from the realization (and disappointment) that he is alive. At the end of the story, it says that "when the doctors came, they said she died of heart disease-- of a joy that kills." They assume that her weak heart could not handle the happiness she felt when her husband walked through the door alive. They do not know- or refuse to acknowledge- the actual cause for her death. Even if they had known that she truly died of shock and disappointment from seeing her husband alive, no one would have spoken it aloud because it was not something that was spoken during that time.
We know that Mrs. Mallard had a very weak heart and that everyone around her was worried about her ability to handle shocks. Although the shock of learning her husband is dead causes an immediate cry, Mrs. Mallard survives this news and goes upstairs. When she learns, however, that her husband has survived the train wreck, that's when the fatal heart attack occurs. It's clear, then, that after realizing she's been freed from the confines of marriage and has her life to live as an independent woman, and then learns that the freedom is gone when Brentley Mallard walks through the door, she dies from the shock of disappointment, not joy.
One of the great ironies in the story is that the people around Mrs. Mallard assume--because of their conventional view of the role of women in this society--that Mrs. Mallard's response to the news is going to be negative. They have no idea what is really going on in her mind. They believe she is, as they expect women to be, fragile, but her fragility extends only to her heart. Her mind is very strong.
The treatment of Mrs. Mallard as a fragile woman who must be protected is very realistic for the time period of the late 1800's. Women simply were not expected to be able to handle adversity the way men were and precautions had to be taken to treat them gently. A less obvious realistic element is Mrs. Mallard's desire to be freed from the repression of marriage. Undoubtedly, there were many women at this time who, if society would have accepted it, would have preferred to live their lives independent of a husband and the institution of marriage and family.