Lemme try to 'splain in, then.
You know how an amplifier rated at X watts into Y ohms is not constantly delivering that wattage, right? Right. So let's say you're listening to the 1812 Overture right before the cannons start to fire. You're on the verge of a huge transient and a huge change in required power. When called upon, the caps will dump their stored energy into the amp in order to meet the needs of the cannons. The larger the capacitor, the more energy it can store and deliver when called upon.
In addition to storing the energy, capacitors also act as filters. Since they sit between your wall outlet and the output stage of the amp, any irregularites in the flow of power to and from the power supply will be smoothed out and not propagated down the line.
