I would say that the primary focus of the title's effectiveness in "The Story of an Hour" would be to ensure that the notion of what can happen in a fixed period of time is conveyed. Chopin explores the entire range of Louise's emotional compass and psyche within the hour she hears of her husband's death and his eventual reappearance. The "story of an hour" is the story of this revelation, of enduring what social conditions dictate and force one to experience and then the personal redemption of how voice can be so powerful that to live without it could be emotionally crushing and devastating. In this sixty minute period, Louise explores and experiences what women for generations have endured, as well as anyone who has been rendered into silence, and the hope that can be felt and dashed in mere moments.
The main character receives some life-altering information and undergoes a thorough transformation during this sixty minute time period in Kate Chopin's "The Story of an Hour." Louise Mallard receives notice of the train wreck with her husband aboard and retreats to her room to first grieve and then rejoice over the news. She fantasizes about the changes that will occur during her expected new life without her husband. The even more surprising news that she receives after she leaves her room concludes the hour of the short renaissance that she experiences. Chopin shows just how fleeting life can be for both Louise as well as her husband.
To me, what the author is trying to emphasize by using this title is that Mrs. Mallard's whole life, in essence, is lived in the space of this one hour. She goes through such major changes in her outlook, all in this very short time.
At the start of the hour, she is a "normal" housewife of the time. She is devoted to her husband and shocked when she hears of his death. But then she realizes that, for the first time in her life, she is free. She lives a different life for the rest of that hour -- it is different from any mindset she has ever had before. Finallly, she is brought back to reality and dies.
So I think that the emphasis is on these huge changes that occur in her mental and emotional state during this single hour.