What is meant exactly by the description 'more musical'?

A good amplifier can be referred to as a musical amplifier. It is not simply a technical term; it expresses how much you love the amplifier.

It's that simple.

In fact, we have our measurement of a good amplifier. If you can continue listening for more than 8 hours, and you still want to listen, that is a good amplifier for you. So, do not judge in a short period of time.

When I think musical I think bouncy and good mid bass. Not necessarily accurate. 

All this sounds simple yet we have many amplifier makers. I suppose most have gotten the "bad" distortion out of their designs, though.

@hilde45 If that were true there would not be a tubes vs transistors debate older than the Internet itself!

Its a bit more complex than that. Many designers don't pay much attention to how the ear/brain system works. So they often just go for the least amount of distortion: your typical solid state amp. Solid state amps have had a reputation since the 1960s of being harsh and bright compared to tubes for the simple reason that the distortion of the solid state amp has unmasked higher ordered harmonics- the source of the harshness and brightness.

Such amps do not tend to get a reputation of being musical and are part of why tubes are still around!

In a nutshell, if i read atmasphere right , psycho-acoustics rule even gear design ...

Not mere taste ....

Van Maanen himself said the same thing as atmasphere ...

https://www.temporalcoherence.nl/cms/en/

For sure different road can be chosen by each amplifier designer, but the road is chosen around the same center : human hearing characteristics ; then putting the emphasis on the way the ears/brain perceive harmonics or the way the ears/brain inhabit his own non-linear time domain; but these differences in design approach will never obey the mere taste of the designer so much as they will obey the specific psycho-acoustic facts and principles by which he will attack the designed "musicality" problem ...

No taste relativity then to begin with and at the end of the design process .., But for marketing taste is first and last , because no design is perfect, marketers will call the customers and spoke to him about his tastes for "musicality" ...But there is not so much taste in the way we evaluate "musicality" as much as different levels and different acoustic aspects of this  complex phenomena ,"musicality", where subjective evaluation is  always conditioned by objective factors ......As musicians and acousticians and trained specialist and maestros or most  designers knows already ...

Atmasphere must correct me here if i am wrong ...

Interesting debate for sure ...