First, It could be not accurate with terms because I didn't major in Korean linguistics.
and my English either...:(
In Korean grammer, We can seperate words in parts called "Morpheme".
there are other parting way to seperate words but Morpheme is the minimum part which expresses meaning.
It means just one missing morpheme leads to break the meaning of words.
When you try to seperate the sentence with Morphemes,
It becomes 섬세하- + 시 + -(하)군 + 요.
섬세하- is the basic form of the verb 섬세하다 used in sentence 섬세하시군요.(※Plz see comment.)
the word means delicate; elegant; sensitive. the term of the part is "Stem of word". stem is "meaning" part of Verbs and Adjectives.
시 is "the Honoric morpheme locates just before ending". It means honor on listener or its relative. Mainly relatives.
It could say that the 시 is not essential part because the sentence makes sense without that 시.
-(하)군 can be added to the end of a sentence that the speaker just came to realize. We can use -(하)군 to end the sentence.
But if the sentence ends like that, It could be rude words. That sentence dosen't contain honor to who "directly" listen the words.
In Korean, The Ending word is most important to express Honor to someone.
If we not use the Hornoric ending and just say 섬세하시군, It could be rude expression. So we end the sentence with 요.
※You are able to not use Honoric Endings only to your friendly, familiar relatives.(Of course with their allowment!)
There are many other Honoric Endings which differ how much honor to listner.
You can see this site if you want to know about -군, -구나, -군요
It would be pleasure if I could helped your study. Good luck!