Functional APIsAPIs are not just for exchanging of data. They provide much needed functionality for developers and integrators. The functionality of an API can provide shipping costs as the Fedex API does, or provide you with directions from San Francisco, CA to New York, NY as with the Google Maps API.
Functional APIs can, as the name suggests, provide much needed functionality to users that might be very costly or impossible for them to implement on their own.
If a developer wants to provide the location of a mobile application user, they need to be able to turn the latitude and longitude of the users position into a physical address, city, state and zip code. This would require creating a massive look-up table of latitude, longitude, and addresses. This wouldn't be impossible, but it would be very costly.
Functional APIs can save developers time when building their applications by providing needed functionality immediately, cost effectively, and with functionality that would otherwise be impossible without an API.