What are App Domains in Facebook Apps?

the app domain is your domain name.

Before you enter your domain, first click on Add Platform, select website, enter your site URL and mobile site url. Save the settings.

Thereafter, you can enter the domain name in the App domains field.

See more at my blog: http://www.ogbongeblog.com/2014/03/unable-to-add-app-domains-to-new.html

To add to the answers above, the App Domain is required for security reasons. For example, your app has been sending the browser to "www.example.com/PAGE_NAME_HERE", but suddenly a third party application (or something else) sends the user to "www.supposedlymaliciouswebsite.com/PAGE_HERE", then a 191 error is thrown saying that this wasn't part of the app domains you listed in your Facebook application settings.