Dual Mono Amp

I think it's mostly to ensure a steady supply of power to each channel. If you hit some steep transients, it's unlikely that both supplies will sag. I think there are also some benefits in grounding and channel separation, but I'll leave that answer to those who know more.

A mono amplified signal is essentially balanced. It sends both a negative and positive signal to complete a wavelength, appose to a unbalanced which sends only ONE signal and the other signal is grounded thus cutting the signal of a single channel in half(equates to less power to the speaker). The difference between a high-end mono amp and a lesser mono amp is that some allow you to have a third wire for grounding the entire speaker which is more of a safety feature then having anything to do with signal processing.

 

Now with DUAL mono amps you have two fully balanced signals allowing you to have a stereo configuration. Unlike an A/B amp which uses a negative and positive signal from both the L/R channels and joining them through a single power supply while outputting TWO individual signals, in this fashion the power output of both channels are cut in half because each channel is sharing a power supply. A/B amplifiers are considered safer compared to a mono because both channels are grounded automatically when the remaining positive and negative signal of the L/R channels are grounded at the amplifier(creating a loop to ground on both speakers). The MONO signal is not grounded unless you have a third connector like you see in XLR cables. this ensures that any spike or voltage cut is sent to the ground and not to any object around it or the power supply itself( this is the safety feature of a balanced signal).

Dual mono amps is there for able to send more power to the Left and Right channels like an A/B.