I think high-end is about believability.
Neutrality is a tricky topic. What is neutral in an album that's recorded track by track, overdubbed, auto-tuned, mixed, remixed, compressed, edited, and messed with through all sorts of filters? If the recording and mastering studios know what they're doing, then you'll get something that sounds like a performance that could have happened in real life, but ultimately it's at the discretion of whoever worked on the album to make it sound believable. Is that then neutral?
I usually define neutral in headphones as something that sounds like a speaker system that's flat 20-20 in an acoustically tuned environment. I've heard a few totally flat systems, and the biggest shock always is how rich and musical they are. Flat sound is not what people think it is (but that's a rant for another time). However, in headphones you have HRTF issues to deal with, and in IEMs you have all that plus fit issues, which complicate things further. If a headphone is neutral to me, is it going to be neutral to you? I have friends with whom I agree almost universally on speakers and full-sized headphones, but with IEMs we're hearing totally different things. So what's really neutral there?
Believability is different, however. You're not concerned about hearing exactly what went on in the recording studio. All you need is to hear something and think, "yes, it could have sounded like that." In fact realism in audio I think is tied to believability far more than actual accuracy.
To get to that point, you need a system that's first of all technically proficient and nails the fundamentals. You're not going to get a believable sound with a messy frequency response, and you need a good deal of resolution, dynamics, and spatial ability. More subtle things like texture (tied to resolution) and tonality (tied to FR irregularities in the mids) are equally important. Most headphones outright fail at that, even some otherwise very good ones. For the few that do, believability is still not guaranteed - you need an extremely high degree of effortlessness, a total lack of grain, and excellent microdetail retrieval, which is something that you may not notice consciously or right away, but which is the difference between being immersed in the music totally or simply thinking "that's a nice system."
I'll be honest, so far I've only heard a few headphones that qualify. The HE-90, the SR-007 for a certainty, the SR-X Mk3 Pro on a good day, and... well, out of my experience, that's it. Mind you, I haven't heard it all, including the HE-60, SR-Omega, and SR-009, which I suspect would probably end up in the high-end category too. Most headphones, though, are very much not high-end.
IEMs are different. I'm not sure what it is about IEMs, but I find it easier to believe in the music with a good IEM even when it's technically not quite as proficient. Maybe it's the holographic nature of balanced armature drivers, or the isolation that helps me get immersed in the music - whatever it is, even simple IEMs like the UM3x, when fitted well, are actually quite close to high-end. They're not there since they fail at some of the fundamentals, but they're quite close.
Again, it's not about absolute neutrality. To be fair, all of the systems I thought were high-end were actually quite close to neutral, but serious deviations from neutrality are generally immediately audible and will detract from believability, ruining the overall effect. But, if you're close enough to neutral, the subtleties are really not important.
Another word you could use is "immersion." High-end systems are absolutely, totally immersive. They will not work for background listening - they will utterly pull you away from whatever you're doing and force you into the music.
I do agree that if you haven't heard it, it's hard to describe what it is. I couldn't have imagined what a real setup sounds like before having experienced it firsthand, and I was a serious musician for quite some time.
On the other hand, all of the above could just as well be meaningless, since mood and setting play into it as much as anything else does. When you're in the mood to enjoy music, your mind will fill in the gaps where the system is lacking. I've enjoyed music on earbuds, a car system, laptop speakers, cheap headphones, whatever have you, and at the time I would not have cared one whit for anything different. Does that qualify them as high-end, or qualify high-end as a meaningful metric?
Anyway, I think it's a pretty nebulous topic at best and something that requires a lot of experience with listening to various systems. Without that experience, and without hearing a real system first-hand, I really think this is hard to talk about.
And now, back to your regularly scheduled trolling programming.