There are two traits that characterize Web 2.0 and differentiate it from Web 1.5. First, Web 2.0 APIs tend to be symmetrical and reciprocal in the sense that not only can data be read out via published interfaces, but can it also be written into those interfaces. This is most apparent when the API is REST-based and supports the full HTTP method set of GET, HEAD, POST, PUT, etc. SOAP APIs can also qualify, and the Web Service Description Language (WSDL) is a necessary component for the discovery of such interfaces.
Second, Web 2.0 APIs are open standards with formal semantic meaning. This, more than anything else, differentiates the applications of Web 2.0 from those that came before. For example, the Amazon Web Services APIs are incredibly rich, but in order to use them a client application must be specifically aware of the AWS protocols and formats. Similarly, in order to use Google Maps, a client application must know specifically about, and code specifically to, the Google API.