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I searched on Google and found nothing specific, so I think you're talking about Web APIs in general, not Android specific.
Given the statement above, I'd say that a Web API is an interface that provide data to several clients.
The client request data from the server, that returns a file in a specific format (JSON, XML, YAML, etc).
The client may be an Android application, a web application from a browser, a server, a script, a batch script, etc.
An example would be an e-commerce Android application that requests a list of products from the server and lists it for user visualization.