'Caucasian' actually refers to a person from the Caucasus Mountains. This is a very ethnically diverse regions, which includes Turkic groups, Armenians and Kurds, as well as endogenous Caucasians like Circassians & Georgians. So its kinda silly to generalize a Caucasian race!
In the 1800's, craniology was used to define racial groups. The archetypal skull for the 'white race' was found in Georgia. Based on this 'scientific' evidence, & some less objective criteria, the German anthropologist Blumenbach used the term ‘Caucasian Race’, to refer to white people, stating, 'I have taken the name of this variety from Mount Caucasus…because its neighborhood…produces the most beautiful race of men.' (Funny that German scientists are always on the looking to prove just how special a race they are. see Aryan)
A broad definition of the term CAN have a practical application, distinguishing a 'white' person (European, MidEastern, North African &some Central/South Asians) from people with distinctly East Asian or African features.
Some use a narrow definition to mean blond&blue eyed (Nordic features, tho not all Nordic ppl are blond) By this defi most Italians, French, Greeks, Turks, are....black? brown?
And the word looses any practical purpose in distinguishing people physically, but retains the greater goal of making Germans feel special.
German to a Circassian:
"Even though your ancestors are from the Caucasus and you have blue eyes and blond hair you're not Caucasian or white" (true story by the way!)
German to an Iranian:
"You're not Aryan you're from Iran...!!!"