For most of the last forty years I've been drawn to high-end audio. When I was a teenager, I pined for a system whose cost was so far out of reach as to not be even remotely possible. Back then I mostly wanted that system because it WAS expensive. I had never heard anything better than the modest stereo I had or the slightly better ones at the local audio store.
Also back then I thought that anything played loudly sounded good - much to the displeasure of my parents. Even in subsequent years, I had entry-level systems I played as loudly as either the system would allow or my ears could stand.
It took me a long time to realize that most of my youthful opinions about luxury audio were incorrect. In fact, today I think that at least one hallmark of a high quality system is its ability to sound decidedly remarkable at lower volumes. I've also learned how important it is to learn how to listen.
I'd say it goes without saying that developing listening skills takes practice. Such skills are not bettered if the system is playing background music while friends are over for dinner. As is part of the audiophile experience, developing listening skills requires a dedicated, serious, critical judgment of the sounds your system produces. Happily, the path to this expertise is why a high end system was purchased in the first place - to listen to exquisitely reproduced music.
Probably most obvious will be soundstage and imaging. Also highly noticeable will be bass response. Is it deep, precise, and has impact or subdued, or boomy? Can the bass line be followed all the way through the song and be distinctly separated from, say, a kick drum or the low octaves of a piano or organ? Are the mid frequency instruments present? Are high frequency sounds sharp and precise or fuzzy and distorted? Is the system tonally accurate overall? Do the instruments sound natural? Is there wide dynamic range and impact? Is the presentation congested or is the background very black? Does each instrument sound like it is in it's own space?
You can also look for transient detail, decay - like you might hear on a cymbal, for instance - brightness or forward, back and, many more. There are also CD's available that identify exactly what should be heard as the song plays. I use one by Sheffield Labs called Sheffield Drive but there are others as well.
In Sheffield Drive's liner notes each song is spelled out in exact detail. For instance, on one song the following was written - "When the cymbals begin to kick in, they can be heard on both channels evenly. At (4:34), there's a distinct stereo separation of one of the drummer's calls as it travels from the right channel to the left." Having this type of information is invaluable for developing listening skills as well as verifying your system's accuracy.
Learning how to listen is an important part of the audiophile process. It serves to enhance our listening experience and possibly even identify weaknesses in a system. It imbues upon the listener a sense of satisfaction, particularly after changes or upgrades have been made. Regardless of system cost, regardless of components, cables, digital, analog, whatever - become involved with the listening process. Learning how to listen takes time and is an acquired skill. Unfortunately, there are not really any shortcuts. Then again, who would want shortcuts? It's why we have a luxury audio system in the first place.