Symfony is a full-stack framework, a library of cohesive classes written in PHP5.
It provides an architecture, components and tools for developers to build complex web applications faster. Choosing symfony allows you to release your applications earlier, host and scale them without problem, and maintain them over time with no surprise.

Symfony is based on experience. It does not reinvent the wheel: it uses most of the best practices of web development and integrates some great third-party libraries.

For further details see at:
Symfony
The Definitive Guide to symfony
symfony API
The symfony Cookbook
Easy Ajax in symfony