Back in the day when I knew all the answers, I was of the opinion that a hi-fi system could be evaluated in two ways.
Firstly by its ability to reproduce, as accurately as possible, whatever was on the recording. This would revolve around matters of low distortion, transparency and dynamic range.
Secondly by its ability to reproduce the essence of the performance, to reproduce the vibrancy of real people playing real music in a real environment.
Clearly both methods have limitations, many of them quite obvious but, strangely, I began to find components and systems that actually appeared to fulfill both criteria, systems that, while clearly accurate to the recording, did not over emphasise the faults and managed to convey the music with a sense of reality that was beyond the simple electo mechanical process of reroducing the data (digital or analogue) of the original recording.
One of the first components that I recall stepping up to this level was the Koetsu Red phono cartriges, then the early Electrocompaniet amplifiers, mid 90s Sonus Faber speakers and a few others. These components appeared to have an almost magical effect on systems lifting them to new levels. Such components and systems became, for me, the 'gold standard' and I considered pretty much everything else to be just mid-fi.
My own proper system has this capability, though by my usual standards has too many limitations on large scale music to be considered real hi-fi. Fortunately, or not, I am one of those people who find that I am uncomfortable listeming to large scale music in a small domestic environment, so the limitations of my sytstem are, for me, easy to live with.