Explain what is a clean power amplifier?

It means nothing more than distortion you can live with.

You will get a slew of answers to the effect that it depends upon measurements. But, that doesn't guarantee an amp will sound good. It's been known forever that tube amps typically have more distortion, but many love the tonality despite them being less clean. 

One man's "clean" amp will be another's "sterile" amp. 

Expect many recommendations of favorites purportedly clean amps. This, as well as any other parameter of sound quality, is on a spectrum - a wide spectrum of performance. 

Just compare a few and go with your favorite. 

No noise and no distortion. 

If you want a really clean amp, I suggest solid state. Tube amps sound better but have too many nooks and crannies that are hard to keep clean.

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.