Surprise! This title refers to the story's duration (an hour) and its actual form (a story). Let's talk about duration first. Obviously, anyone who sits down to read this is going to finish a lot sooner than someone who sits down to read a full-length novel, like Chopin's The Awakening. Short stories are generally smaller in scope than novels, so it works well for the subject of "The Story of an Hour" to be limited to events that can happen in only an hour's time. We can read about the things that happen to Mrs. Mallard in just about the same amount of time that it takes for them to happen, which is pretty cool. This lends the whole thing a sense of immediacy – in other words, a feeling that things are happening to Mrs. Mallard right as we read them.
An hour doesn't seem like a lot of time – it's barely an episode of The Vampire Diaries. As soon as it starts, it seems like it's over. An hour, though, can seem like it goes on forever if you're doing something difficult or uncomfortable – like go to the dentist, sit in detention, or if you're on a road trip and desperately looking for a decent public restroom. In Mrs. Mallard's case, processing the tragic news of her husband's death and what it means for the shape of her life makes that hour slow way down and stand still. It may not seem like it takes very long, but a lot of stuff happens to Mrs. Mallard during that hour.
And what about the "story" part? This literary work is both a story and a "story"; it's a story Kate Chopin wrote and a "story" Mrs. Mallard lives. In the title, "story" both describes the form of the tale that Chopin is telling about Mrs. Mallard, as well as the "story" Mrs. Mallard tells herself about the potential her life can hold, once her husband has died.
Yet this title is not exactly what Kate Chopin named this work when she first published it. She originally called this tale "The Dream of an Hour" (source). In this more original version of the title, the idea of emphasizing the duration of the tale still applies. But the more self-referential aspects of the "story" aren't there. Instead, Chopin refers to Mrs. Mallard's experience during the fateful hour as a "dream."
The use of "dream" instead of "story" makes Mrs. Mallard's thoughts during that hour seem even more fanciful and less realistic. It seems like Mrs. Mallard, in thinking them, has less control than she would if she was authoring them as part of a "story." A dream is more ephemeral than a story – you can't hold on to it, you can't reread it like you would a book or retell it with as much recall. A dream escapes. And that's what happens to Mrs. Mallard's briefly imagined ideas of her future by the last line.