Hi. I just posted a reply to your earlier question under "rhythm." To me, being "musical" is how much or little we are actually responding to the music -- as opposed, say, to just using it as a time keeper like a metronome. Are we breathing with the music and meshing with it?
I often take class now ("open adult" ballet classes) that has live piano accompaniment and am amazed at just how unmusical some can be. I recognize that in some cases maybe they're struggling with a step or placement issue, but sometimes I just want to stop the class and scream, "Can't you hear where "one" is!?" Or, "Can't you tell that if you keep going the way your going with this combination, you're going be four measures behind and run out of music?!" Clearly, some are better than others at this. Part of the fault (if I can say that this strongly), lies with the teachers who in walking a class through a combination, be specific enough about the counts and then insisting on keeping with these benchmarks, if the students get off the music (which can be easy to do). So if an arabesque is supposed to be struck on count 6, for example, and some get there early or late, they are not called on this, so end up being off the music, and so "unmusical."
And none of this takes into account phrasing, which is a whole other ball of wax!