It's evident that there is a connection between telling a story and being a great leader: business writers frequently describe famous CEOs as master storytellers. Most give only a vague sense of what it means to tell a story (or sell a story) and why it is a key ingredient of leadership.
In groups of people, the natural leader is the person with the strongest outcome. Outcomes (goals) are a source of tremendous strength: they provide a clear path for people to follow, and people will follow that path unless they have a compelling reason of their own for choosing a different path. The clearest path is the path of least resistance: it attracts all the flow of energy that is not already moving through a channel. The strongest outcome wins.
What is the strongest outcome? It is the outcome that is most fully imagined: the one that includes the most sensory detail, the most complete ecology check, and the best sense that it is possible to get there from here. The form of that imagining is the story. Stories are narratives that include sensory detail, multiple view points (through the inclusion of multiple characters and influences) and a movement from where they start to where they finish. Stories are outcomes with legs: they not only describe, they move.
Leaders tell stories: they present rich, multi-dimensional visions that move from the status quo to a different reality. When they tell their stories, they give followers a map that allows them to progress imaginatively towards an outcome, and then to follow thier imagination with real steps towards achievement.
Learning to form the strongest outcome means learning to form outcomes that are stories. Learning to be a better leader means learning to tell better stories or to tell stories better.