Explain what is a clean power amplifier?

OP, study what signal to noise ratio is, that is a relatively quick way to determine if an amp is "clean".

Also, as others mentioned, don't focus too much on "cleanliness" in amp measurements as that attribute won't necessarily tell you if you will like how a particular amp sounds.

With regards to power line noise, on a separate front from distortion, that is not the amp but the electricity that runs it, and a truly clean amp probably has a good quality power supply that does what is needed to feed the amp clean power it needs to perform well. If not external power conditioning should help or be an insurance policy at minimum.

True that both noise and distortion makes an amp "unclean".  The amp itself produces both to various degrees aside from the electricity it runs on. 

The horror!   What a mess!

Amps that are not clean, just need an intervention.
Once clean, they can relapse  But so many amps are in denial.  

Nordost QX4. Enough said.

The devialet expert 120 I'm selling is one CLEAN sounding amp!