capacitance in power amplifiers designs, At least the capacitance that I would assume you are reffering to being power supply filter capacitance, pretty much goes like this...
This is reffering to a traditional Linear power supply... as found in nearly all amplifiers.
The power supply of the amplifier does just that, supplies the power. First it goes through a transformer which (usually) reduces the voltage from 120v to what the design needs, it then goes through diode rectifiers that will take the negative half of the sine wave and, in essence, flip it to make it positive. As seen in figure 3.
As you can see in the picture diagrams 1 and 2 are what it looks like before the rectifiers, And once rectified, Then the filter capacitors come in. They are what fills in the gaps between the "bumps" Capacitors are like a battery, in that they can store energy. The amount of energy is determined by their capacitance rating (and voltage rating) Capacitance is measured in Farads. A farad is a very large amount of energy so in home audio applications a usual spec you would see is say 15,000 microfarads, which is just a fraction of one farad. The difference between a capacitor and a battery however is that a capacitor dumps its entire amount of energy nearly instantly. The energy that is store in the capacitors is used to fill in the gaps in the sine wave to make (ideally) a completely flat DC voltage, pictured on the very bottom of the diagram. In a poorly designed power supply you would get something more like figure 4 with a certain amount of ripple. This is undesireable.
Not only do the capacitors fill in the gaps but they also add to the amount of current that the power supply can put out during musical peaks requring large amounts of power, more than can even be supplied by the wall outlet at any one time and because that extra reserve is there ready to be released in an instant. The bigger the power supply is the more power is going to be available. MOST power supplies i have seen, in my opinion are not sufficient enough to be called good but because of cost and size requirements many times sacrifices are made in the design.
Hopefully that gives you an idea of what it does without getting too technical.