The Google Ventures blog has a great article discussing the value of using storytelling to avoid the trap of designing individual, disconnected screens.
The best product designers practice story-centered design. They begin by crafting stories that show how customers interact with a product, and only after they’ve accomplished that do they design screens as a way to tell that story of interaction.
By telling a story about your users and the problems they're facing, storytelling - and related techniques such as story boarding- can help your team better understand the problems needing solved, as well as draw attention to the weak parts of the story - the spots where the problem isn't well defined and additional user research is likely needed.
Employing storytelling is a great way to make sure you're solving the right problem for the right people, and that you have enough information to approach the solution smartly.