API = Application Programming Interface. This is the way other applications can communicate with Piwigo. This feature is also know as Web Services.
This documentation is under construction: not all methods are described here. You won't have to find methods by yourself in Piwigo source code, we have a web API browser, distributed in Piwigo itself. On any Piwigo installation, go to http://yourdomain/yourpiwigo/tools/ws.htm from your web browser and discover all methods. For example web API browser on Piwigo.org demo.