From the Facebook Newsroom:
The App Center features mobile and web apps, such as Draw Something, Pinterest, and Nike+ GPS, and new apps including Jetpack Joyride, Ghosts of Mistwood, and Ghost Recon Commander.
The App Center gives you personalized recommendations, and lets you browse the apps your friends use. It only lists high-quality apps, based on feedback from people who use the app.
To make it easier to find social apps for mobile, the App Center isavailable in the Facebook iOS and Android apps, as well as Facebook.com.
Every app in the App Center has screenshots and a detailed description, so you can learn more about it before installing it. It helps you control your privacy by showing the information an app needs and letting you choose who can see your activity on Facebook. If you decide you want to use an app, you can get started directly from the App Center.