Hi Defiant,
Power supplies provide a (hopefully) fixed voltage to the circuits which does work for us. Say, +15VDC, Ground and -15VDC is typical for a solid state preamp / CD player, etc.
A "perfect" power supply has no output impedance. No matter what the circuit it feeds does, the voltage remains rock-solid.
As the output impedance of the supply goes up, the voltage sags and surges as the demands go up and down respectably. So, instead of exactly 15VDC, it will start to look like 13V to 15V, tracking the output signal somewhat. The higher the PS output impedance, the more this happens.
Once this happens, your power supply has a "copy" of the music. This is where cross-talk happens, as well as weak bass and reduced dynamics. If the L channel is moving the power supply V, the R channel will be influenced, and vice-versa.
One of the best Ideas I ever read about was a designer who would listen to his power supply. He would treat the + and - rails and hook them up to headphones or speakers, so he could literally hear the noise or cross talk in the power supply itself. Pretty brilliant.
Best,
E