Facebook Connect is a login platform that lets users sign into sites or services that aren't Facebook, with their Facebook credentials. This means they can enjoy most or all of the benefits of being a registered user for that service, without the need to sign up and provide things like e-mail addresses, or any other personal information. Instead, that log-in is going through Facebook, and the user has controls over what that site can do all in one place.
Since opening up in late 2008, Facebook Connect has been growing in adoption. Most recently it's been integrated into the popular Digg.com. It can also be found in a multitude of Apple iPhone applications, since Facebook launched a portable version of it back in March.