The whole idea of a power supply in audio electronics is to convert the alternating current (A/C) from the wall to direct current (DC). DC current is required for anything regarding audio (it just cannot run from straight A/C like some motors can).
The reasoning behind creating a separate power supply will vary depending on manufacturer. In a nutshell, a separate power supply will shield the core audio circuits from the electromagnetic noise caused by the transformer in the power supply. Generally it is not really a problem, but it can cause a slight buzz in the audio if the transformer is too close. The second reason could be that the manufacturer just did not have the room to build in the power supply they wanted within the size of the preamp chassis. A good example of this is the Krell 202 preamp:
http://www.hifishock.org/gallery/electronics/krell/preamplifier/
You can see from the pictures that the power supply is enormous with two large transformers and a lot of transistor heatsinks for their shunt regulated DC power supply.
The alternating current AC from the wall comes in waves that run at 60 hz (about 60 waves per second) where half the time the voltage is "pushing" and the other half it is "pulling". DC requires a 100% constant "push" in voltage that is one direction only. The power supply tries to "leak" the current pressure from the AC and also store as much voltage in the power supply capacitors so that it can continue to provide a 100% DC current even when the AC is not pushing current at all (which is between the waves).
The size of the power supply can also dictate how good of a sound quality you get. With regards to extremely large power supplies, it can help further smooth out the sound. My research and experimentation has shown that conventional circuits and op amps do not really require a huge power supply. However, when you start using Class A type audio circuits, then the power supply size becomes hugely important. The Class A circuits require a large amount of constant current and you can actually reduce the sound quality by providing a "too small" power supply. You are actually starving the audio circuit and the end result could be things such as a thin/bright/harsh type of sound. A prime example of this is the older Krell KAV-280p preamp. This is also similar to the Krell Phantom III preamp. They both have such a small power supply with limited capacitance (4 x 3300uf in the 280p) that the sound is bright/thin. I found that doubling that to 4 x 6800uf significantly changed the sound and it was no longer bright/thin - had a tremendous amount of bass and midbass strength. When you get into the larger Krell preamps, such as Phanton II or Phanton I, you will get the larger power supplies for very similar audio circuits.