Mark, as Ian and Chris point out, what you were referring to is
termed "slew rate". This is the rate at which the amplifier
changes voltage level over time. The usual parameter is given in
volts per micro second. When a frequency during music appears
which is higher(faster)than the previous frequency or is louder,
the amplifier has to supply more voltage because of the higher
level and do it more quickly because of the higher frequency.
This is needed to produce that note at the required level and
with low distortion. Note that this has nothing to do with
sharper transient response or a perceived "tighter, quicker"
sound; it's just doing the frequency accurately with low
distortion. The required slew rate at any instant in time is
given by 2 x pi x freq. x voltage(peak). For example, to
reproduce 20,000Hz at 100 watts(i.e. 40V peak, 28V RMS for 100
watts into 8 ohms, since power equals
voltage(RMS)squared/impedance)the slew rate would be about 6.28
x 20,000 x 40 = 5,240,000(in micro-volts)or a slew rate of 5.