Authentication is what happens when a user is logging into your site. When a user is created, an authentication method must be chosen for that user. This can be changed for the user later.

Moodle offers a variety of ways to authenticate users. You'll find them under Administration | Site administration | Plugins | Authentication | Manage authentication. Each of the options is briefly explained by clicking on Settings for that option:

The following subsection will fill in some key information to make it easier for you to work with these authentication methods.