the 12Volts to that connector provides voltage to the "field" of the alternator. The spinning alternator rotor in this magnetic field, is what causes the generation effect of the alternator. If you do not hook this 12 volts to the "field" of the alternator, all you would have is a spinning hunk of iron...
The one wire aftermarket alternators have this built into the alternator, but most require a certain speed to "start" the alternator. Most see this when they have to rev the engine right after startup to see the alternator kick on. (ie right after startup a voltmeter will read just 12 or so volts - essentially battery power....when you rev the motor and bring the alternator up to proper speed, it will start generating, and your voltmeter should read 13-14 volts.)
Not sure if I am gettting the point across... /forums/images/graemlins/dunno.gif