This new feature of Facebook helps developers showcase their apps and also helps users find Facebook compatible apps they can use on their smartphone.
All you do is go to the Facebook App Center at: http://www.facebook.com/appcenter. You’ll see a list of recommended apps and apps that your friends are using.
You can search through games and other apps.
Once you find the app you want to download, just click the “Send to Mobile” button.
If you have push notifications turned on for your Facebook app, you’ll receive a notification that the app is available for download. Then when you open your Facebook app on your phone, you’ll see the app listed on the menu.
Click the app and your phone’s app store will automatically open, so you can download the app.