Explain what is a clean power amplifier?

Clean is a subjective term. 
What is a “clean” house?   No house is perfectly clean.  It’s just a matter of how much dirt one tolerates.  
With amps it’s distortion, not dirt.   All amps have some.   Can you hear it?   If not it sounds clean.   
Also all amps produce more distortion when they have to work harder so as the distortion goes up they become less “clean” sounding. 
At some point they all run out of juice and clip.  That’s when things really start to become a mess. 
Hope that helps. 

I have found my McIntosh power amp sounds better with an inch of dust on it than when it is clean😂

Disconnect the pre-amp and keep the amp connected to the speakers.  turn the amp on.  Any noise?  no?  That is one level of clean.

If there is noise, then the amp or the outlet voltage (or both) is definitely not clean

now connect the pre-amp to the amp, turn them on.

Noise?  No.  Raise the volume on the pre-amp.  noise?  then something is not clean.  there really should be no noise at full volume with no signal.  some tube pre-amps do have noise and high volume.  

Play some well recorded music.  first, there should be zero noise through the system with no signal.  When you play music, it should sound accurate.  musical instruments should sound like real musical instruments.

If it sounds distorted or off, then it isn't clean.  if there is noise, then it isn't clean.  However, in listening to music, it may be not only the amp, but the other components that are contributing to the unclean sound.

A low levels, it should be "clean" accurate reproduction of the signal.  you should be able to hear and distinguish the music very well, even at low levels.  At higher volumes, it should remain "clean" and accurate and sound off.

enjoy

It's like the Woody Allen joke."Is sex dirty"? "Only when done right"!

Clean power coming from an amplifier ,comes first from the electrical grid of the house....

Then it is of no avail to bought the best amplifier in the world without cleaning the electrical grid....

Costly solutions exist, but low cost one also....

When the power that comes from the grid is cleaner, a better instrumental timbre and a better imaging result naturally from the conveying signals...

Instead of thinking about how to embed their amplifier or any other gear, most think to buy a ready made solution... But there exist NO electronic component that is by itself the ready made solution to the complex triple embeddings....

« Noise contains silence like oyster contains pearl» -Groucho Marx