One of the most powerful reasons to prototype is the value gained from having a something tangible for stakeholders and customers to interact with. This is especially true for mobile app prototypes loaded on device.
Shiny presentations and click-through demos are valuable and important to include in your process, but they allow stakeholders to be removed, forcing them to imagine the way the interaction will behave. In their hands, they will have first hand experience with your design, and understand not just the micro interactions but the wider context and flow.
Show and tell is similar to the usability tests you can conduct with the same prototype, the only difference is the audience. There are many questions that stakeholders might raise when looking at your design, and some of these questions are part of the validation phase. Often this breaks down between the how and why. Before showing to customers and understanding the why, the prototype can answer stakeholder how questions. How does a button work? How does it scroll, load, animate between states and views?
Your prototype help also with gathering stakeholder feedback. It may be your prototype is more a proof of concept you will use to socialize a new feature or improvement. Consider how easy handing a phone to a colleague and letting them play with your prototype compared with booking a meeting or walking them through a full demo.