The serpentine belt is a flat drive belt that snakes around all of the different components in your engine that need auxiliary power such as the alternator, the air conditioner, the power steering fluid pump, the water pump, radiator fans, etc. If the serpentine belt breaks, then the aforementioned components will not work and your engine will not function properly. Unlike a broken timing belt, a broken serpentine belt does not cause irreparable engine damage; however, your car is not drivable until you have the serpentine belt replaced.
A serpentine belt is essentially a long belt that is flat on one side and often has ribs or nubs on the other side. Check your serpentine belt for two things: wear and tension. If the belt is dry, cracked, worn, missing ribs or glazed (shiny), then it needs to be replaced. If the belt 'gives' more than a half inch when you press on it, but is in otherwise good shape, you might be able to adjust the tensioner to make it tighter. If you hear a loud squeaking or chirping noise coming from your engine when you accelerate, odds are you need a new serpentine belt. We recommend replacing the belt and tensioner simultaneously - the parts aren't that expensive and often the air conditioning condenser or radiator needs to be removed for access.
Since belts wear out over time and you are stranded when one breaks, we recommend changing them every 50,000 miles or whenever indicated by your owners manual.