The purpose of IndieAuth is to provide a means to log-in to other websites using your own identity (e.g. your domain) that's independent of other authentication methods such as via a Facebook, Twitter or Google log-in.
Authentication through IndieAuth can be achieved through a number of methods however probably one of the most straightforward is to use a website called IndieAuth.com. It provides a method for authentication known as RelMeAuth. This is a specific authentication method designed to use with your domain that's implemented by using the relme attribute for hyperlinks to places that represent you on the web.