"Easy Auth" is what the Authentication / Authorization feature in App Services is called.
The idea behind this is that you can have an Azure website and using this feature you can add authentication to it with a few clicks,
You do not have to use NuGet OWIN packages or anything similar. No code is involved.
Essentially it uses an "agent" feature as per Architecture of Azure App Service Authentication / Authorization. There's a native IIS module that sits outside of your application and all requests are directed through this. If not authenticated then you get redirected to the Azure AD login screen. (Recall that Azure web sites actually run on IIS).
You don't not have to add an application to Azure AD. It's all done for you.
So how does it work?
I used VS 2013.
New Project / ASP.NET Web Application. Ensure MVC is checked.
Click the "Change Authentication" button and select the "No Authentication" radio button.
So now we have a bare-bones project with no built-in authentication.
Now deploy to Azure (there are tons of posts around this so I'll skip the details).
At this point you have a web site - e.g. https://easyauth.azurewebsites.net/.
There is no entry for this in Azure AD.
In the new portal, click on "App Services", then the app service (the web site) and then "Settings".
Select "Authentication / Authorization" as above.
Turn on Authentication. choose "Login with Azure Active Directory" from the drop-down and then click the "Azure Active Directory" authentication provider.
Then select the "Express" setting.
Now if you go to the old (classic) portal under "Azure Active Directory" you'll see that you have a new application.
You should be able to navigate to your website and the first thing it should do is ask you to authenticate.
Except - it doesn't!
Back to Mr. Google and I found this: How to configure your App Service application to use Azure Active Directory login.
As per the section: "(Alternative method) Manually configure Azure Active Directory with advanced settings", you need to click the Advanced section (not the Express) and add:
to the "Reply URL" in Azure Active Directory. Don't worry about all the stuff about actually creating the application - that's already been done.
And then, lo and behold, it worked!