A power supply converts the AC wall voltage into something useful for our audio equipment—typically DC.
That conversion process of AC to DC sounds simple enough that we might imagine they are all the same, yet that would not be true—which is why many audiophiles have strong opinions on what's best. Some are happiest when their power supplies are made from massive hunks of steel and copper festooned with a forest of capacitors. Others are thrilled when a thousand watts slip out of a tiny switch mode power supply without all the iron and parts of the aforementioned linear supply.
Yet, we don't listen to power supplies. The sound of DC is zero. If you connect a battery to the input of your amplifier (don't do it) no sound should come through the speakers.
Power supplies make no music, yet they are one of the most critical elements in a high-performance audio product. This is because they are the source of what follows. The amplification circuits are simply modulating the power supply in cadence with the input signal. The more rock-solid, low noise, and perfect the power source, the closer to live our music will sound.
Power supplies, and the power feeding those supplies, can often make more difference in sound quality than the circuits they feed.
If you're the type that dive's deep into a product's technology, it's equally important that you consider the power supply serving the amplifier.
A great amp is only as good as the power feeding it.