This article is from the Car Audio FAQ, by Ian D. Bjorhovde (firstname.lastname@example.org) with numerous contributions by others.
The headlights will dim because of a momentary drop in the voltage
level that is available to power the vehicle's accessories, including
the headlights, amplifiers, the engine, etc. This voltage drop can be
caused by a very large current demand by an accessory, such as an
amplifier trying to reproduce a loud bass note.
The first thing to do is to get your battery and alternator checked for
proper functioning. A failing battery can place undesirable loads on
the alternator, leaving less power for your system.
If the power system appears to be working correctly, an improved
alternator may be required for the large current demands of the audio
system. When upgrading an alternator, be careful in your purchase, for
there are some potential problems. An alternator which advertises a
certain output level may only achieve that output at very high engine
RPM ranges, for instance. Also, the new alternator must be adjusted to
provide an output voltage within a reasonable range in terms of the
If you find your car will not start after playing the stereo for long
periods of time with the engine off, and the present battery is in good
working order, then another, paralleled battery could prevent this