Get yourself a real voltmeter that plugs into the power port. Or for us old guys, the cigarette lighter socket. Watch what it does when the light comes on. The not running battery voltage should be 12.4 or higher.
Start the car and the voltmeter should read 13.8 or so. It can get as high as 14.5 or so. When that light comes on, if the voltage reads battery voltage or about 12 volts your alternator may need replacement. The belt may also be slipping so that should be checked before alternator replacement.