The alternator is the electrical power plant for your vehicle. It powers everything from the headlights and radio, to the computer controlling the engine. Late-model vehicles are operated by computers in various locations in the vehicle. These computers must the proper voltage to operate normally. A failing alternator can cause symptoms ranging from a dead battery, to stalling, to gremlins such as your wipers turning on by themselves.
Many times a faulty alternator can be the result of a weak or failed battery. The battery can cause the alternator to become overworked, making it fail prematurely.
"My battery light is on..."