Capacitors hold a charge for a certain period of time, even after the power is cut off, and it dosnt take much to charge them... They are not only charged while they are supplied with voltage... They act as buffers for energy basically... And how they work on your stereo is, while your stereo is on and your battery isnt being strained (no loud bass hitting, and the amp trying to pull tons of power from the battery), the capacitor is being charged upto its capacity (measured in farads)... And once its full it continues to hold that amount of power, and when the amp draws more power than you battery can give, the capacitor supplies the amp with the required power, and then when the battery isnt being strained again, it will charge back up and store the energy until the amp requires it again... It basically just acts as a buffer for energy...
They are the main reason, why your not supposed to open up electronics, even after you unplug them...
And to back up what I am saying...
From this link:
http://www.uoguelph.ca/~antoon/gadgets/caps/caps.html
A healthy, good quality capacitor (disconnected) can hold a charge for a long time. From seconds to several hours and some for several days depending on its size. A capacitor, in combination with other components, can be used as a filter that blocks DC or AC, being it current, frequency, etc.
Also note that a weak battery, already being drained, will probably not be enough to power the whole system... Hence why Tankard still had a problem, and had to replace his battry... So replacing the battery with a new one, will definately help... But the capacitor will help the new battery to not become so less drained...
So basically, both sides are right to a point...
But yea, if your lights dim, its a sure sign you might need one... Either that, a new battery, or an alternator... They will both solve the not enough current/power problem... Remember, anytime u add an electrical component, you are working your alternator harder, so it does have a better chance of dying out sooner than it would normally... But me, Id worry about that when the time comes, and just get a capcitor now, if that dosnt help then Id get a new battery... And since capacitors all do the same thing, brand name is not an issue... Size is, and 1.5 farad is plenty...