The techology is called PWM; basically a digital signal is "transposed" to Pulse Width Modulation with no feedback. Essentially the speaker is driven by pulses of power, not a continuous wave. The inertia of the drive is sufficient that the cone operates as if it was driven by any normal amp. But in a sense, the speaker is really the DAC, here.
"Digital" amps are extremely efficient, turning 80%-95% of input power into output power. Since very little is lost as heat, they typically run much cooler than A or A/B amps. And the processors are fairly cheap, although obviously the companies who've made their living selling boat anchor A/B amps churn out very expensive Class "T" and Class "D" amps.
Digital amps can be made very small, allowing you to put high quality amps into places you normally couldn't (flat panel monitors, clock radios, very small cell phones, etc). Low power consumpion is a big plus for these devices. It also allows fairly powerful amps to run on batteries, freeing you of some AC related noise problems.
