class D is a form of switching amplifier, and work on averaging some pulsed output. a switch is a lossless device as it is either shorted (no voltage across device) or open (no current through device). thus, amplifiers that ONLY make use of the on or off state will be more efficient.
but the amp's output is analog. so averaging is done using a passive filter. basically, the speaker has no possibilty of moving in and out 100,000 times per second, so the rapid switching is ignored. but if the switching devices are on longer then they are off, there will be a higher then 0 average output, and the speaker can respond to this.
The filtering creates delays, and has resistance, both have adverse effects on "negative feedback". as such, some class D amplifiers have poor damping factors compated to class AB amps. bandwidth is usually better then quoted, but becomes distorted at higher frequencies. modern class D amplifiers are overcoming both the damping ratio and bandwidth issues, allowing for full range sound.
in terms of "digital", some class D amplifiers are moreso then others. for instance, the output is very similar to a 1 bit DAC, and the PWM generator is a lot like a 1 bit ADC, but the lack of a clock degrades this interpretation. some class D amps use a clocked PWM, making this analog to digital to analog discription more accurate.