It's important to know whose story it is because that's the person we as readers will focus on. We see through their eyes, we feel through their emotions, we are scared when they're scared, happy when they're happy, in love when they love. We want to make the connection, and if it's not there, or confused, we disengage. Sometimes the story is written through a single person's viewpoint about the events in their lives, so it's obvious where our focus is. Sometimes the story is told by an outside observer and it's less clear whose story it is. A good example is The Great Gatsby. The plot follows the story of the relationship between Gatsby and Daisy, but the story's really about the narrator Nick Carraway and how he changes over the course of that summer.
Sometimes I see stories told from the point of view of a character who doesn't change, who isn't affected by the unfolding of the tale, so why should I be affected if they aren't? This is something to check when you're revising, whether you've written a short story or novel: have you chosen the right point of view? Always go for the person who is changed the most by the story.
*She has gone on to be multi-published, with very focussed stories so I imagine something stuck!