Literally, high fidelity, as in getting the most information out of the recording and presenting it in the way the recording artists intended.
How do we know exactly what is really "the way the recording artists intended" considering the industry has no standards and the artists seldom have knowledge about the capabilities of the high-end?
That is indeed a fascinating question. Also, how can we ever truly know if we are hearing exactly what is on the recording? It is interesting that this is the stated goal of quite a few people in this hobby. This might make a good thread topic for a different discussion.
I haven't thought this all the way through so I may change my consideration, but, for the moment, I'm very leery of this question being useful. We see the question (posed rhetorically) a lot, often mid-squabble. It's kinda an expression of sheer scepticism that can be used to thwart any attempt to come to a conclusion. We also see it associated to a list (Ron's ?) of 4 Types of Audiophiles, one being those who seek reproduction true to what is on the recording, or some such.
Microstrip's formulation (above) taken from Dave C's cue asks about the artists' intent. This is somewhat problematic because intent is difficult to gauge through listening. If they're still around, we could ask performers - "does this recording exhibit what you intended?" Suppose they say 'yes' or 'no' - what does that tell us? That the recording is faithful to their idea of what they wanted it be? Huh? What does that tell us?
Inspired by remembering that Descarte's scepticism ("How do I know that I exist?) was ultimately the cause of his certainty (cogito ergo sum), I'll rashly answer the question. :-O
We start with the notion that at such-and-such a time and place the XYZ Orchestra of the Air along with The 4th Street Belmont Singers performed Brahm's Schicksalslied Op.54 and that was captured by microphones, etc. and put on tape.
There was an act of recording; the verb. But is that 'the recording' ? If it is, all the scepticism boils down to saying we cannot relive the past, so we can't really know. Even if we could, that's not the recording of a performance, it is the performance.
Is the so-called 'master tape' the recording? No, it's a magnetic tape on a metal reel. Even if you hold it close to your ear you won't hear the Song of Destiny. Not even a pre-echo.
I reject the notion that "the recording" exists as some kind of timeless objective Platonic Form that is The True Recording, that it is something we can never truly know, something that at best we can only grasp as 'shadows' of the recording. This seems to be the angle where the question is coming from.
Music is performance art. It exists in time and is transient. A recording must be performed to hear music. It moves from the potential (media) to the actual through time - when the recording is performed, when the record is played. Every time you play a record you hear exactly what is on the recording.