I am going to hazard an explanation based on my limited knowledge of HT, but I may be wrong
Let us assume for a moment that the input signal is digital (coax/optical from a cd/dvd player).
Traditional receivers or dedicated amps have class A/AB amplifier sections. These amps amplify the input signal by using vaccum tubes/transistors. However they work in the analog domain which means 2 things -
1. the input must be converted into analog using a DAC (digital to analog converter)
2. analog circuitry to amplify this signal and convert it into a voltage to drive speakers. This process is very power hungry, innefficient and produces a lot of heat. This is where the weight of traditional amps and special design features in costlier amps comes from.
Both 1 and 2 cause signal degradation and introduce imperfections in the original signal, especially as the volume is increased.
A digital amp on the other hand operates totally in the digital domain (I believe they are class D). There is no need for a DAC, and the signal is amplified digitally using PWM (pulse width modulation). Near the speaker terminals, it is finally converted to analog using a simple low pass filter.
For an analog input digital amps have a ADC stage just before the amp.
Typically all this is done using a mass produced IC like TI's equibit which is used in the Panasonic products.
The benefits are high efficiency, much cheaper cost, and most importantly higher signal quality, irrespective of the volume.
All of these are why the digital amps sound so much better than traditional ones.