The things that jjss49 and knighttodd mentioned describe what I'm looking for the most.
If I were to add anything to their statements, it would probably end up looking like this:
"Music reproduction that has great clarity and precision, a rich/full/natural tone, realistic articulation, plus the ability to immerse me into a believable 3-D listening experience - and on top of all that, to do it all at lower volume levels."