Interesting question, might mean different things to different listeners.
On the “Chesky Ultimate Headphone Demonstration Disc” the very first track “When the Saints Go Marching In”, can you focus in on each individual instrument when all are playing in unison, can you follow one of the instruments to the exclusion of the others, and can you hear and keep track of all 6 players simultaneously as well. Notice how the high hat cymbal strikes at the end of the drum solo lose intensity with each successive hit? These qualities may seem obvious but the more I listen (to any music) the more these aspects become clarified for me as a listener, up to a point. And when I evaluate a new piece of hardware I’m listening for those fine points And then there are those times when a new piece of hardware in your system suddenly reveals something you never heard before. But, that case could also be a factor of that new piece providing an emphasis in an area that wasn’t emphasized before, and that could be a right or wrong thing especially if it interferes with some other aspect of the sound to it’s detriment (to your way of hearing it).
On the second track “Don’t You” can you sense the bow strings “rubbing” on the cello bodies strings? Can you sense the vibration of the wood body. Does the violin have a “juicy” quality to its sound? How about Amber Rubarth’s voice? How about the hand slaps on the drum? How real do they sound?
I listen primarily to classical music (and acoustic jazz) which, in many cases, may utilize up to 100 musicians. How easily can I follow one instrument or group of the same instruments through the overall texture of the other instruments especially when all are playing in unison. Does the recording capture the air and space, the reverberant qualities, of the recording venue which are generally unique from one location to the next. Can I hear an occasional chair squeak, a page turn, a conductor shift his/her weight on the podium. Spotlight mics provide high-lighting of certain instruments and can vary from one recording to the next and can affect overall balances from one recording of the same work. These micro details are a quality of the recording captured by the engineers, and can vary with mic positioning, type of equipment used, producers/conductors expectations for a sound design, the acoustic qualities of the recording venue, and I’m sure there are other factors as well and is one reason why, along with interpretation and ensemble execution, classical listeners will generally have several different recordings of their favorite works.
(An Aside: I have read that some composers of classical music, especially large orchestral compositions, don’t score the music with the expectation that every instrument will be clearly heard at all times. Sometimes instrument(s) are employed to provide a sense of weight, color, atmosphere, rather than being obviously, there.)
With popular genres, usually a recording release is a once and done, plus maybe a “live” performance recording. Perhaps someone else more knowledgeable in popular genres could better answer this. But I think the rules are still the same; if you know how many players are involved and is it a studio or “live” recording, what are the finer details you hear with repeated listening? And with a live performance recording how well do the balances bring out everything there is to hear?
The more times you listen to a recording, the more familiar you should become, and the more fine details you should be able to hear, up to a point. And here is where your playback equipment becomes a determinant as well. And then there is the psychological side to music and listening to it, there are many books on the subject.
I’m not sure if my answer helps you or not, but that’s my take.
Happy Listening