This article is from the Car Audio FAQ, by Ian D. Bjorhovde (firstname.lastname@example.org) with numerous contributions by others.
A capacitor serves to smooth the voltage fluctuations associated with
transient current draw. As a result, the supply voltage presented to
the amp during peak demands tends to be slightly higher than without
the capacitor. For most amplifiers, this will increase the power
output of the amplifier during transients. The degree to which it
increases, however, typically leads to an inaudible improvement.
To illustrate, if you consider an amplifier that delivers 100 watts at
14v and 80 watts at 12v (these numbers are somewhat typical), the
difference in output from the speaker will be at best 1 dB when the
supply voltage fluctuates from 14v to 12v. However, when you take into
account the fact that no practical amount of capacitance can completely
eliminate this voltage drop during transients, the difference in output
becomes even less pronounced. Further, if you take into account other
factors such as loudspeaker power compression (discussed elsewhere in
the FAQ), the equivalent series impedance of the capacitor, the length
of the transient, and the human's decreased ability to perceive
differences in intensity for shorter intervals, this difference in
output becomes negligible.