Charles Wiltgen: The best definition of web services that I could find was written by Doug Tidwell of IBM:

Web services are a new breed of web application. They are self-contained, self-describing, modular applications that can be published, located, and invoked across the web.

Web services perform functions, which can be anything from simple requests to complicated business processes. A simple web service might provide stock quotes or process credit card transactions.

Once a web service is deployed, other applications (and other web services) can discover and invoke the deployed service.