Without trying to sound too technical, Web Services are software components that are accessible on the Internet. Web Services are reusable and are available to both applications and web-site developers. Typically, the casual Internet surfer does not use web services directly, but he / she is likely to benefit from them by using an application or visiting a web site that does use Web Services. When an application or web site incorporates a particular service, the service is invoked when called upon. The Web Service could return a weather forecast or current stock exchange information. Or, the Web Service could return a map. For more information on Web Services and mapping, please visit Web Mapping Services in Geomatics.
For more information about Web Services in general, please visit the World Wide Web Consortium's site. It is an extremely informative site that discusses a wide range of Internet protocols and standards.