What is meant when someone says a component is lacking soul

IMO, "lacking soul" means flat or blurred dynamics possibly accompanied by alack of transparency and / or harmonic detail.

True musical detail is most often a matter of electronics that possess very accurate timing.  

It does not have to sound clinical or uninvolving to lack soul.  I build a DHT preamp that has a selector switch so you can use five different resistors.  Each one has a plus and a minus to the sound.  I found the naked Vishay to be very open and detailed, the Audio Note very sweet, Carbon was musical but kind of boring sounding but good for poor recordings, Shinkoh was emotional sounding, involving so maybe it had more "soul" and the Caddock was what I preferred in my system, kind of had it all.  With the Shinkoh you really felt like you were there when a singer really dug down deep.  You could really hear the effect of the singers lungs expanding and air rushing out so it was emotional sounding to people who heard the preamp when I switched resistors.  So IMO, more "soul".  The other resistors sounded excellent but in direct comparison were lacking in "soul".  Hope this was helpful.

Happy Listening.

Lots of great descriptions here!!!

"Soul" should be a term more relevant as to not need a separate post to receive a definition. 

I equate "soul" being the human element of sound reproduction almost exclusively regarding vocal reproduction. 

Any instrument played by a human being can reveal "soul" as the specific musician allows their creative individuality based on their emotions to shine through in their singing/playing.