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

I’m going to add to what @mapman has pointed out. Musicality has everything to do with how the amp makes distortion. The main differences we hear between amps, their ’sonic signature’ is in fact their distortion.

To be musical, that distortion has to be benign to the human ear. The only harmonics that qualify in that way are the 2nd and 3rd.

Higher ordered harmonics, the 5th and above, are sensed by the ear and interpreted typically as harshness and brightness. In musical instruments, the higher orders are sculpted by the instrument maker as the tone colors of that instrument. IOW distortion is sensed by the ear in the same way that the ear hears tonality in musical instruments.

Fortunately, if the 2nd and 3rd harmonics are high enough in amplitude compared to succeeding harmonics, the latter can be masked. The result is even though the higher orders are present, the presentation can be smooth and detailed, which is to say ’musical’. Tube amplifiers are very good at this sort of thing, which has kept them going the last 70 years. Solid state has been challenged by this issue because while they typically make less of the higher orders, their higher orders are not masked.

The ear is keenly sensitive to the higher ordered harmonics because it uses them to sense how loud sounds are. The ear has over 120dB range and frankly, a lot of solid state amp designers didn’t take that bit into account, so unmasked higher ordered harmonics will cause the amp to be harsh and bright; i.e. not so musical.

This is a bit of a nutshell description of the issue.

You'll know it when you hear it. 

some amps are about the sound; meaning you are more aware of pieces of the sound....bass.....detail.....high frequencies.....maybe impact and aggressive beat. it might sound very clean and even scrubbed a little. note decay can be clipped. certain electronic music is complimented by this presentation. these amps strangle the music to a degree. clinical.

a few amps are about the event, the intensions and artistry of the performers, the vibe of the venue, and immersion into the rich tone and textures of the nuance and feeling of the musical energy. the beat might not be as impactful, but it carries you along more into the essence. these amps get out of the way of the music. musical.

there is more to these things than amplifiers, there is the context of the speakers, room and system....and the type of music and quality of the source.

but amps do play a big role. this is not a tube<->solid state thing. but it is related to simplicity of circuitry and keeping the processing to a minimum. zero negative feedback helps. efficient speakers help. a great first watt helps. the music can’t be held back.

some amps can be musical, but too colored to be effective with all types or scales of music. but that might your preference. personally i want an amp to sound like music, and not have any sameness of coloration i have to listen through.

+1 @mapman

I have resisted the term, because whatever someone prefers in the character of their system is going to be the one which draws them into the music, no?

If that’s true -- and I cannot see how that can be disputed -- then every system which someone likes is "musical."

What if someone’s ear does not care about the kind of distortion @atmasphere identifies with musicality? Would we say their use of the term "musical" is incorrect? This would be tantamount to saying that "good food is spicy food" and then for anyone who demurs, they like "not-good" food. Would we say that some people like "not-musical" amplifiers?

That said, I do see that some here are trying to help associate the word "musical" with its most frequently used associations -- lexicography, if you will. It's "rhythm and pace" or "2nd and 3rd order harmonics," etc. Maybe that's useful. I'd still expect a lot of people to just use the word to mean other things, and not really be incorrect in their usage. This makes the word of suspect usefulness.

What if someone’s ear does not care about the kind of distortion @atmasphere identifies with musicality? Would we say their use of the term "musical" is incorrect? This would be tantamount to saying that "good food is spicy food" and then for anyone who demurs, they like "not-good" food. Would we say that some people like "not-musical" amplifiers?

@hilde45 No, what I described is based on rules of human perception, which encompasses all people. This is the same reason that deciBels are used, why humans are thought to have a range of 20Hz to 20KHz and so on.

What you are describing is 'taste'. I was not. If amps are not musical, no-one likes them. They might tolerate them; that's different. You can tolerate something but be annoyed by it at the same time.