Issue #4 of the OCLC Newsletter NextSpace has a nice, clear introduction to the concepts of Web Services and why they are important: Moving to the network level. I also liked the quotes they pulled out as illustrations - I put one of them up on my wall.
Functionality traditionally installed and run on a local computer in a single application is now performed on the network inside workflows that involve many applications. In essence, the Web becomes the “operating system” to which programmers write reusable, constantly updated software components that are delivered over the network and embedded or loosely coupled with other Web applications.
The most popular method of combining, or exposing, these modular applications is through Web services. Web services allow different applications from different sources to communicate with each other without custom coding using emerging Web protocols. The services are not tied to any one operating system or programming language.
Thanks to CISTI's Mike Ireland for pointing this article out.