Facebook only allows the login functionality to work on sites that use https/SSL. You'll need to access your site over https for the authentication feature to work.
If you don't have an SSL certificate, we recommend looking into CloudFlare. They are free, speed up your website, add security and provide your site with SSL (https) encryption. It's the easiest and cheapest way to add https to your site.
I hope that helps, but if you need anything else, please let us know.
Thanks,
Alex