You will hear fine details that are otherwise not audible on a lesser system.
Bass - How tight or loose the bass is (including but not limited to its style and textural resolve) Can be described as boomy, full-bodied, etc. and of course being able to discern bass extension etc.
Midrange - It should sound like being inside the microphone, capturing the very same tonality and extension as the singer’s voice. Sharp or peaky female vocals should, for example, bloom naturally. Like in Diana Krall's - Black Crow. With other artists, you can almost tell what they ate just before recording etc.
Midrange/instrumentals - being able to establish the relationship between vocals and instrumentals. How prominent or recessed are the instrumentals? Do they ever overpower the vocals; or do they instead act as a perfect backdrop to elevate that performance? Are there fine details that were reproduced slower, rather than faster? This is telling of a resolving audio system.
Treble - Like midrange, it should be extended and bloom naturally. Sharp peaks, dips, and even unpleasant-sounding treble frequencies should coexist organically, with the rest of the spectrum. A cymbal that wasn’t recorded or mixed/mastered properly on a track will sound artificial, papery...not metallic enough and with recessed attack/decay/fade out. )
Brilliance (uppermost treble) - The "air" so to speak in a recording. The space between instruments. The tempeature of the air in a room, which results in a overlay that must coexist with overall tonal balance. Not enough during post-production can result in a track that sounds too "digital" or congested.
Perhaps put together some reference tracks and compare/constrast? I know quite a few that can help...