A capacitor is added because batteries are slow to give up charge, relatively speaking, and are slow to recharge, where capacitors are nearly instantanious. Think of it like eliminating a speed bump in the road.
Your amp demands current, to really slam a huge instantanious explosion or bass drum... in that instant, it exceeds the current capability of your alternator, so it must draw the extra current from the battery... the battery is like Droopy Dog.. it's saying "Ooooohhh... kaaaayyyy... heeeeeerrreeeesss yooouuurrr currreeeennnntttt", and finally the amp gets the current. But there is a rise time involved. Granted it is tiny, but here's where the lightning fast capacitor can help out. It gets rid of that speed bump. While waiting for Droopy Dog, your capacitor discharged for the amp.
Capacitors are also good, in scenarios where you have fast kick-drum type bass. They don't help much at all on those long drone-tone extended bass tones like bass CD's, like sine waves, but that's fine... they don't hurt performance in those scenarios, either.