A little background: I have the opportunity to present the idea of a public API to the management of a large car sharing company in my country. Currently, the only options to book a car are a very slow web interface and a hard to reach call center. So I'm excited of the possiblity of writing my own search interface, integrating this functionality into other products and applications etc.
The problem: Due to the special nature of this company, I'll first have to get my proposal trough a comission, which is entirely made up of non-technical and rather conservative people. How do I explain the concept of an API to such an audience?