If your question pertains to complication as part of a plot graph for the story--the part in a drama that would be called the rising action---then the complication covers the action between the inciting incident and the story's climax. The inciting incident ends the story's exposition and begins the action.
In "The Story of an Hour," that point seems to come with the news that Mrs. Mallard's husband has died. Her reaction to the news of his death constitutes most of this story. The climax of this story, which ends the complication, happens, of course, when an particularly unexpected event occurs. Thereafter, Chopin provides only a brief period of falling action and a very short denouement or resolution.
"The Story of an Hour" has a couple of complications in it, depending on how you read it. As the story begins, Mrs. Mallard's friends are concerned about having to tell her that her husband has been killed. She has a heart condition, and they're afraid the shocking news will cause a heart attack. So they very carefully tell her what happened, and they leave her alone for awhile to deal with the news.
What they don't know could be considered another complication from the friends' point of view. Yes, the news is shocking to Mrs. Mallard, but it is not so unpleasant as her friends thought. She has felt penned in by her husband for a long time, and now she sees the chance to live for herself.
There is another complication, but if I tell you what it is, I'll give away the end of the story.
If you need one overriding complication to answer a teacher's question, you might say it's Mrs. Mallard's lack of personal freedom and the limits put on her by her health and by her husband.
one hour of freedom worths a whole life of dominance and repression
the position of women patriarchal society where men dominated and controlled women unfairly