The Battery Light circuit turns the alternator ON and OFF, yes alternators have an on/off switch, otherwise they would drain the battery when engine was off.
On the 3 wire connection on the back of the alternator, there will be a Light Green/Red stripe wire, that's the on/off wire, it runs to the Battery Light.
When you turn the key ON the ignition switch sends 12volts(battery voltage) to the Battery Light, then thru the battery light to the Alternator(LG/R wire), the alternator is now on but if engine isn't running, the alternator is 0 volts(a ground) so Battery Light is ON, current is flowing.
When you start the engine the alternator produces 13.6v(approx.) so system is now 13.6v , at both sides of Battery Light, so no current is flowing thru the bulb and it is OFF.
If alternator voltage ever drops below Battery Voltage(12v) then Battery Light comes on again, current is flowing thru bulb.
Battery Light circuit has a 500 ohm resistor in case bulb burns out, so alternator can sill be turn ON and OFF.