Here's a picture I made. It might help you visualize the diferent "phases" of electricity. The three colored line corespond to the three primary colors used to label the standard three phase power used most places. The second chart shows standard 110/220v 60hz power.
Why a neutral in a three phase system? Weeeelllll since most gear, dimmers and
amps included, actually run off of 110/120 you need to allow for that provision. Having a neutral allows you to get 110 power out of even a 208 system. Notice that in a 110/208 three phase system the voltage potential between ground <earth> and any hot leg < phase A,B or C> is still 110volts.
Where does the hum comes from? wellllll notice the time line the voltage "flips" 60 times per second, another way to say "times per second" is Hertz, or Hz. So a poorly grounded system can allow sympathetic, wave forms to show up in the final output of the sound gear, and lights. you don't notice it in the lights because of "Persistence of Vision" , but your ears are attuned and can hear the resultant 60 hz signal comming out of the speakers.
I'll follow all this up with the statement Icewolf made, feel free to correct me, y'all.