Zeitgeist is a PHP based multi purpose framework for web applications.
Originally developed as a framework for web based browsergames, Zeitgeist has since then grown into a framework for any kind of web application. However it's focus is still PBBG (persistent browser based games) or other highly pipelined applications.
The idea of Zeitgeist is not to be a full blown framework with a ton of modules and purposes. Instead it offers a set of very generic classes that cover a wide range of possibilities. With them you can develop applications in a short amount of time.
The repository contains the framework itself (including test cases) as well as examples and a demo application. It also includes a tool to administer and set up new Zeitgeist based applications which is based on the framework itself and doubles as a demo implementation.
If you want to dive right in, you should read the Quickstart tutorial.
If you want to learn more in depth details about Zeitgeist, you should start at the overview page.
If you want to get started writing games with Zeitgeist, there is a tutorial that shows the creation of a simple browser based game.