The Graph API from Facebook allows you to interact with a user’s profile and other data on behalf of that user. In order to gain access to some parts of the API (such as viewing posts or posting for the user), you need to submit your app for approval (which involves making a screencast demoing the app). I’ve seen a varient of this question:
In order to demo my app I need permissions to read posts and post for the user, but I can only get them by going through the approval process. How can I demo the app if I don’t already have the permissions?
Posted on SO and a few other sites. The answer is to either use test users or the developer accounts associated with your application. You can ask for and grant any permissions to test users while your app is still in development mode. Move through the approval process with these test users and take your app out of development mode only after approval has been grated to ask real users for these permissions.
You can create and manage test users by following the documentation here.