PHP extensions allow modifying and extending the PHP language. There are different types of extensions including wrapper extensions for interfacing with C libraries, speed and algorithm extensions for optimizing slow code, and Zend extensions for modifying the PHP engine. Writing extensions requires knowledge of C, the PHP internals including zvals and the PHP lifecycle, and using tools like phpize to generate the extension scaffolding. The document provides guidance on setting up a development environment, writing extension code, and testing extensions. It also outlines best practices for extension coding.