Which component is most responsible?

This has to come from the source or else nothing downstream can put back what was lost. Massed chorus music and complex full orchestra passages are extremely challenging to the entire audio chain so that it all needs to be right or else muddiness results... much easier to get distinctness with a few "voice" lines than many competing voice lines

Which component(s) is most responsible

Components is correct, all of them. As Davide256 said, "This has to come from the source", then the preamp/amp must do its job to drive the speaker with this quality created by the source, and the speaker must be able to reproduce this quality. Just having all high quality components/speakers will not assure that you will achieve this quality. Synergy between components/speakers is extremely important as well.

I disagree about the 'source' theory. I have heand the clarity of separate voices in a choir, or individual violins in various systems. and most of them had 'ordinary' sources. Cheap Cd players.. Generally the ones which can 'do' the job have a good preamp, a stellar amp and great speakers.
I heard this phenomenon first time back in 1984 when I listened to Carmina Burana auditioning speakers in Chicago with Infinity RSIIa speakers (EMIM units in there) Powered by a Onkyo Integra amp, the big one. And a Integra preamp. Ordinary second generation $400 CD player. No special wires or anything..

So I challenge the 'source' folks to explain it...
Maybe it was a 'magic' CD player?

Now it is true a great source can sound marvelous.. But many cheap ones can sound really fine with great maps and speakers. (Maybe they just never heard a good inexpensive source?)

It's how it was recorded. Either the recording has or it doesn't. If it does, even a moderate quality system (with attention paid to setup) will reveal this effect.

Onhwy61 beat me to it, but to hear distinct separation of vocals requires the microphones to be placed in the optimum locations to achieve that effect.

It always tickles me when someone defines this or that component as having great imaging because they can hear the location of each instrument on the stage. If it was not recorded that way, you will not hear it that way.