To answer this question from my understanding...
An authentication system that uses REST so that you do not need to actually track or manage the users in your system. This is done by using the HTTP methods POST, GET, PUT, DELETE. We take these 4 methods and think of them in terms of database interaction as CREATE, READ, UPDATE, DELETE (but on the web we use POST and GET because that is what anchor tags support currently). So treating POST and GET as our CREATE/READ/UPDATE/DELETE (CRUD) then we can design routes in our web application that will be able to deduce what action of CRUD we are achieving.
For example, in a Ruby on Rails application we can build our web app such that if a user who is logged in visits http://store.com/account/logout then the GET of that page can viewed as the user attempting to logout. In our rails controller we would build an action in that logs the user out and sends them back to the home page.
A GET on the login page would yield a form. a POST on the login page would be viewed as a login attempt and take the POST data and use it to login.
To me, it is a practice of using HTTP methods mapped to their database meaning and then building an authentication system with that in mind you do not need to pass around any session id's or track sessions.
I'm still learning -- if you find anything I have said to be wrong please correct me, and if you learn more post it back here. Thanks.