When your alternator warning light is on it means that your voltage is not right or the alternator is faulty or the alternator is about to go out.
If your alternator light comes on it's usually an indicator of a faulty or failing or already failed alternator.
If your alternator light comes on you need to have your alternator and voltage system checked out through a shop or I think Autozone can even check your alternator out to see if it's going bad.
An alternator light coming on could be indicating that you have a faulty battery as well.