I was one of the presenters are a post-conference workshop at the SharePoint Conference in Anaheim, CA this past October. When one of the other presenters, Donovan Follette, took the stage, he started discussing claims based security. He first started out with a great scenario based description of what it was. For me, it was the best and most clear explanation I had ever heard. Afterwards I asked him if he would please blog it so I could share it with others and point folks to it.
Just recently I got a copy of a new SharePoint + Azure book (more on that in a moment) and saw a chapter on claims based security. Sure enough you could tell Donovan wrote this as it was the same scenario. Over the weekend I noticed that Donovan also posted his description in a post on his blog! So, if you're confused about claims, you need to check out his post: Professional SharePoint 2010 Cloud-Based Solutions by WROX! - Overview of Claims-Based Identity.
I also want to call out that this is another great resource on integrating SharePoint 2010 & Windows Azure. A few months ago I blogged about another book out there (Developing Microsoft SharePoint Applications Using Windows Azure). Well, here's another one that also involves Steve Fox (the author on the first one):