In 2012, Credits were worth 10 cents each (with a sliding bonus scale when you buy in bulk). They work just like arcade tokens. You can buy them on Facebook using credit cards, PayPal, gift cards, your mobile phone (the purchase will go to your wireless bill) or at various retail stores depending on what country you're in. Since Credits are virtual money purchased with real money, you keep them in a virtual wallet -- linked to your Facebook account.
Facebook maintains a long list of games and applications that take Credits. Some require Credits to play or use, but the majority simply use the Credits system for add-ons within the software. For example, a Farmville-type game might use Credits to purchase additional turns or rare animals, while more competitive games against other players could take Credits to give you offensive advantages. You can buy Credits both within a game or application by going to your payments tab.
Your purchases, account balance and payment methods are available for review under the payments tab in your accounts settings. Since younger people and those without credit cards can use other methods to purchase Credits, it's important for parents to monitor their kids' purchases. This is also one reason the site maintains purchasing limits, just in case something -- like an enthusiastic kid or a Credit-hogging hacker -- slips through the cracks. If you want to change your payment method, keep kids or others from using your Credits, or block certain payment methods from being used in your particular situation, those settings can also be accessed from the payments tab.