Stories have the power to persuade. Let's look at advertisements, which sometimes follow a story-like narrative structure. Researchers Quesenberry and Coolsen (2014) asked the public to rate 108 Superbowl commercials from the 2010 and 2011 Superbowls. They then coded the commercials to designate if they followed a dramatic structure or not. I think you already guessed that overall, commercials that were stories were favored over those that were not.
Advertisers want to persuade you. Stories help them to achieve this.
And what is more powerful than changing someone's mind?
How about letting someone believe the conclusion you want them to come to is their own?
Stories allow us to communicate and give advice indirectly. They allow the listener to come to their own conclusions- conclusions that the storyteller has the power to guide them to. We can sell our ideas through stories. They also tap into emotions, which even for the most logical person, play a big part in our decision-making.
You can read about how gratitude is important as a motivator at work. But numbers and statistics won't have the same impact as a story about the impact of gratitude, such as the story below.
For more information on this idea of stories for persuasion and real-life examples of how stories can change behavior, see the Harvard Business Review's article, "How to Tell a Great Story."