What is this term 'analytical' ?

It usually refers to a set-up that emphasizes treble/high frequencies. If you listen to a lot of live, unamplified music or play live music yourself, you soon find that a lot of audio systems.do like to give you a bit more treble.

A boosted treble/high frequency response giving the impression of detail at the expense of timbre and tonal contrasts.

It’s an old trick that often succeeds in gaining the listener’s attention.

Hi-Fi journalism is littered with such anecdotes as the following, " I’ve heard this track countless times but I’ve never noticed X or Y before."

The only place you might need this elevated response is in monitoring where you want to put a spotlight on possible issues especially in the so called presence/brilliance bands up to 9 kHz.

It is generally agreed that the industry favourite Sony MDR 7506 headphones employ this frequency response for exactly that purpose.

In domestic audio its a sure fire way to discover the dreaded listener fatigue.

I would say equipment having all the detail up to fault presenting music not as a whole but somehow independently. I would not confine it into highs region only and is rather a subjective term commonly not expressed in a positive manner. Some people can call it detail, accuracy, neutrality but these are softer expressions leading to analytical if in excess.

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.