PHPBuilder has posted an excerpt from an Apress book today - "Beginning Ajax with PHP: From Novice to Professional". It's from the third chapter that introduces the PHP and Ajax combination.

While the concept of Ajax contains a handy set of functionality for creating actions on the fly, if you are not making use of its ability to connect to the server, you are really just using basic JavaScript. Not that there is anything truly wrong with that, but the real power lies in joining the client-side functionality of JavaScript with the server-side processing of the PHP language using the concept of Ajax.

The article's pretty light on the code, but it does give a full example of showing and hiding dynamic content pulled from a backend PHP script (calendar information). Outside of that they just discuss general topics like "Why PHP and Ajax?" and the difference between client-side and server-side processing.