What is a 'fast' amp?

fast 'rise time' or a fast waveform response vs a slow one.
Look at the square waves in test teports.
A 'fast' amp has a near vertical rise in the squarewave. A 'slow' amp has a curved line in the vertical response to a square wave.
Some amps start out the squarewave with a steep, near vertical line and 'tire out' and start to curve off on the rise.
Some cannot maintain the power and curve off the square top of the waveform towards the far edge.
The graphic chart is not all there is to a power amp, but the response to a squarewave tells a lot about how robust the circuitry really is. Advertising claims aside.
What the 'fast' means in sound is powerful transients. Crisp attack.
Slow means warm. Sound is rounded out. mellow.

Wow, good description, Elizabeth.

If you want to hear what's on you album or CD, would you rather hear as closely as possible what's actually recorded or something smoothed over?

Think of it this way. An amp is taking in what's coming to it, amplifying it and passing it along to the speakers. The faster a good amp reacts, the more realistic your presentation.

It's called the amp's Slew Rate. If you've heard about Class 'A' amps, this is their bread and butter. If an amp is running wide open all of the time, it can react much quickerto the input.

The problem for the user is that the amp is drawing a lot more current from your wall outlet because it's running at full power all of the time. It's also why the amps run warm to hot.

Krell has tried to make this more efficient. You can look into Class 'A' and Class 'AB' amps more if you want to.