What is this term 'analytical' ?

A system that emphasizes the details of music loosing midrange emphasis as well as rhythm and pace (think musicality / the emotional connection). So the tick of a drumstick against the cymbal is highlighted but voices are typically subdued. Typically a trait of  older and less expensive solid state (not tubed) audio gear. 

High end audio for those that care to pursue it has a very large vocabulary. It takes a lot of exposure to music and to the nomenclature to learn and connect the two. If you are interested, I recommend Robert Harley’s book The Complete Guide to High end Audio. This is an excellent place to start and a reference to reread occasionally.

Good thoughtful answers. Seems like it means what I might think of as bright, or top heavy.

Now if someone would tell me what 'musical' means, and how it's different...

Who knows the brilliant Mingus (I think) quote?

All together now: 'talking about music is like...' 

Too sterile. also, boring with no character....you want/need some warmth to make it more enjoyable over the long term. Too bright can be characterized as fatiguing and full of sharp ssss’s... That’s just my opinion. Musical in my book is if your tapping your foot. 

Emphasize trebled and blunted dynamics.

Agree with audioguy85. You’ll know it when you hear it. The sound is lifeless, sterile, not engaging, boring.  It's different from bright, to my ear anyway.