When they hear a good story, listeners say, 'oh, that reminds me ' and launch into their own stories. Once a set of stories is amassed, more formal approaches such as observation, structured interviews, and task analyses become easier. At the same time, the process of collecting and telling stories can help users feel more comfortable as participants in the design process. Storytelling can break the ice, and make more formal processes like structured interviews a bit less threatening. Stories also work well as a way for promoting collaborative work and understanding within the design team.
Stories are a sort of equalizer.
It doesn't require much expertise or training to listen to and tell stories. Team members from any background can be made part of the process of telling and collecting stories. And once stories have been gathered, team members can discuss the stories, argue about their interpretation, and generate hypotheses about what users' problems, needs, and practices. This process sensitizes everyone to the usage domain, helps people identify questions and issues to probe for when they talk with users, and best of all provides concrete examples which can prove invaluable when team discussions threaten to veer into debates about vaguely defined abstractions. The collection and generation of stories happens most during the early stages of design, and serves as a precursor to more formal analyses.