Please go to the
Facebook Developer Area
and click into your application.
At the top of the page should be a switch for "App Mode:" with options of "Development" or "Live". Make sure the slider is in the "Live" position.
While in development mode, only developers or admins of your Facebook application will be able to login. Once you set the switch to 'Live', then any visitors to your page can use authentication.
I hope that helps, but if you need anything else, please let us know!
Thanks,
Alex