What are web services ? The World Wide Web Consortium defines them as software systems designed to support interoperable machine-to-machine interaction over a network - which is accurate yet all-encompassing.

What do Web Services mean to Web 2.0 ?

Web services are simply the tools allowing us to develop online web / network accessible offerings within the overlying concept of Web 2.0 (ie. a seamless, integrated, customer-focussed network of useful applications). 

Web services are the tools which bring the Web 2.0 focus to life.