oAuth is an open protocol that provides an authorization mechanism for clients/third parties to access resources on a server, after being given permission by a user.
For e.g. You have photos on a photo-sharing site (server), and you (user) permit a social networking software (third-party) to allow access and thereby show these photos.

oAuth requires the server to authenticate the user before they present the option to let a user authorize the resources.

oAuth is used more in B2C scenarios, and a third-party is an authority between the user and server. This basic scenario is called a love triangle, and there can be many servers involved in the middle for authentication, called hops.
http://oauth.net/ has all the details.

oAuth is implemented by a number of vendors like Facebook, Twitter, etc. and is usually used in an application integrated with these third parties. These are the “authorities” that issue access tokens, and accept them (in the future) to verify access.

If you are have an integration with a third-party which implements oAuth, you could avoid 1authenticating your user, and just rely on the third-party. The assumption here, of course, is that your user is registered on the third-party provider’s website.
If you need, your website can also implement oAuth and be an authority to grant access rights to third-parties.

Other possibilities that involve third-parties for verifying a user include:

– Active Directory Federation services – This is a Microsoft protocol that allows a single sign-on mechanism for websites. You can read all about it here: http://technet.microsoft.com/en-us/library/cc736690(WS.10).aspx
Microsoft Passport is a provider.

– LDAP – http://www.gracion.com/server/whatldap.html, which is usually used by programs and for lower-level resource access like printers, etc.

– OpenID – There are many providers including google, yahoo, flickr that support openID as a standard way to authenticate users on the web.

– WS-Trust and WS-Federation – Used more in Enterprise scenarios, a Provider of information such as a Healthcare company or a bank can be an authority and use WS* to allow third-parties access to the data. Read about it here: http://msdn.microsoft.com/en-us/library/bb498017.aspx

Hope this and the previous post gives you some possibilities to think about, when it comes to authentication and authorization on your websites and applications.