Facebook Applications are made to enhance your experience on FB with amusing games or useful features. One part of the applications are built by the FB developers, but other part are built by independent developers. You can easily play social games simply alone or with your friends, share your taste in music or movies, send gifts to friends, and much more. If you want to learn more about an app before you grant it access to your information, you can visit the App About Page for that application.
You can discover new Facebook Applications and Games easily at the Application Dashboard and Games Dashboard. You can view here the latest applications or games which you (or your friends) have used. The Games Dashboard (left navigation column) is a dedicated for you to receive updates from your games to remind you if it's your turn in a game or to let you know that a friend has taken an action in that app.
You can easily manage, block/unblock, remove an application/game at the Application Settings page (Account -> Account Settings -> Applications). You can also remove annoying posts from an application at Your Wall by clicking on the X at the top right corner.