SharePoint 2013 Authentication

The following are the new Authentication features in SharePoint 2013.

Feature	Description
Claim based authentication	User authentication in SharePoint 2013 will be based on Claims, the classic Windows Based is being removed, though it is available in the Preview version, it will be removed when the product is released. We can switch from the classic mode of authentication to the Claim based authentication by using the new Convert-SPWebApplication Power Shell command. SharePoint 2010 which allows migration of authentication modes based on web applications only, SharePoint 2013 allows migration based on content databases also.
Support for OAuth 2.0	SharePoint 2013 now supports authentication based on Open Authorization 2.0 (OAuth 2.0) protocols, this authentication is used to allow temporary access to a limited set of resources like lists, images etc. Support for OAuth now simplifies the process of server-to-server authenticating and App authentication.
Distributed Cache server	SharePoint 2013 introduces a distributed Cache server which enables caching of user credentials in a centralized location used in multiple Front End Servers.

To know more about the Authentication features in SharePoint 2013 refer the following posts.
SharePoint 2013 Claim Based Authentication
SharePoint 2013 Support for OAuth 2.0

SharePoint 2013 Distributed Cache Service


Related Post
SharePoint 2013 Hardware and Software Requirements
SharePoint 2013 Authentication
SharePoint 2013 Sites
SharePoint 2013 Communities
SharePoint 2013 Content
SharePoint 2013 Search
SharePoint 2013 Insight
SharePoint 2013 Composites
SharePoint 2013 Claim Based Authentication
SharePoint 2013 Support for OAuth 2.0
SharePoint 2013 Distributed Cache Service

Forms Authentication

In Forms authentication the user is provided with a Security Token which will grant him access to an Application / Service.

Initially when a user tries to log into an application, he is redirected to a login page where he will have to enter his login credentials (username / password), the users credentials are validated with the user database, if valid then, and a security token in created and attached to the current HttpContent, the security token is passed back and forth for every successive request the user makes to the application which enabled him access to all the pages until he logs out.