Its operation started yesterday
It offers users access to over 600 applications including mobile and web based apps with names like Nike + GPS, Ghost Recon Commander, Jetpack Joyride, Stitcher Radio, Draw Something and Pinterest.
The Facebook App Center will use "smart" technology in the background to suggest to users the applications they would like to install. This means that everyone will be able to see and install applications used by their facebook friends.
Also, in order for the user to install an application on his mobile phone through the Facebook App Store, he must either select it from the Facebook mobile app or from the Desktop there will be the option "Send to mobile", then Facebook will send a link to his mobile phone. which will lead to the corresponding App Store.
Finally, as in all App stores under each application there is the necessary description as well as Screenshots. The Facebook App Center is expected to open for the rest of the world in a few weeks.
You will find the Facebook App Center at facebook.com/appcenter.