What exactly is a digital amp?

The digital amp has an output stage working on constant switching from 0 to 1. For every 0 and 1 there's a specified output voltage and current. The signal is primerely being broken by the clocking circuitry that defines the switching ratio of an output stage.
The higher the clocking freequency is the higher precision and clarity of a digital amp you'll get.
The main benefit of digital amp that it's always on the stand-by mode and "waiting" for the command of cloaking circuitry thus being not affected by heat dissipation losses and very efficient energy consumer.

Daltonlanny,
Class H is a digital amp.
I still don't know all the differences between classes higher than D.

The main benefit of digital amps is bass since lower freequency get substantially less distortion when sampled or clocked. Bass region is the most power demanding region of amplifier and speaker. I know of Tact gear as being pretty smart developed technology allowing the amplifier to be switched onto a bunch of different classes of operation that is controlled by a proccessor which allows to maintain the low distortion parameters throughout the large freequency and dynamic range.
The pure digital amp nowdays maynot approach the advantages of conventional A, A/B classes of operation unless the circuitry sophistication is applied.