Function
The inline release at the end of the controller contains a USB port that plugs into your Xbox 360, and easily detaches if a player pulls the controller too strenuously, to avoid jostling or tipping the console.
Solution
Retail stores don't carry replacement inline release cords, and you can't buy them directly from Microsoft. Some online vendors sell it under the name "breakaway cable," for 60 cents to $11, plus shipping, as of November 2010.
Fun Fact
Inline release cables are universally compatible on Xbox 360 controllers, which means you can switch out the cord from a broken controller to quickly get back into the action.