The 'Cap' is a Capacitor. It is used for a couple of reasons. the Car electrical system is often very noisy and voltage may fluctuate quite a bit. The Capacitor will help smooth out the electrical disturbances as well as provide a very quick resonse to power spikes needed by a large amplifier. They are not absolutly necessary as most amplifiers have them built in, but typically the internal ones are not as large as could be needed. Most amps have built in switching power supplies that step up and regulate the voltage to the internals of the amplifier and they can draw huge amounts of current, and this my friends is where the larger external capacitors make your system kick! Also you can find the new craze of 'digital' capacitor. Which is basically a couple of standard caps with some 'soft start' circutry and maybe some Blue LEDs. check with your amplifier manufacture they should have guides on what size you will need. And always used heavy gauge cables for amps direct to the battery.

TypeR pretty much covered what a cap is. In short, a cap is installed between your battery and amplifier. A cap stores up energy from your battery and ensures that your amplifier gets the power it needs to hit those loud low notes. A capacitor is usually only installed on a subwoofer amp since they often require a more significant "jolt" of power compared to an amp powering your mids and highs.

If you have an upgraded audio system in your car and your headlights dim each time the bass hits, then you could definitely benefit from a capacitor.

As for how big of a cap, here is a general idea:
.5 farad cap for systems up to 500 watts.
1.0 farad cap for systems up to 1000 watts.
2.0 farad cap or more for more than 1000 watts.

A cap acts somewhat like a small reserve battery for the audio system, generally the subwoofer. It stores the energy and releases it much faster than a standard battery. Also there are "bat caps" a battery with internal technology letting it release it's energy very fast like a cap, but having the capacity of a battery. Another new technology is a "hybrid capacitor" using new internal components. it is still a capacitor, but is rated for higher capacity and acts like a small batcap. Ther are capacitors available from .5 farad to over 50 farad, and batcaps that are rated at over 200 farad. Also be very careful installing a cap as wiring it wrong can and most likely will result in more than a small spark, they can explode.