There was a time when my airbag light would stay on, indicating a sensor identified a problem somewhere in the car. When this happens, the airbag is effectively disabled, meaning you are screwed if you get in an accident. Before I ever took it to a shop to get checked out, the light stopped staying on. Apparently, it is an issue with our cars that many have experienced. If it stays on when you drive all the time, it is worth getting looked at. Otherwise, it may disappear in a week.
Continuous Air Bag Indicator - Diagnostic Trouble Code Timed Out, Diagnostic Monitor Disconnected or Inoperative, or No Ignition Voltage to Diagnostic Monitor.
Mine came on at about 20,000 miles. It was the air bag module itself. Ford replaced it free ($250) because the SRS parts have a 5 year, 75,000 mile warranty.