Someone highbrow is highly cultured and sophisticated. You can call such a person a highbrow.
Certain types of art are considered sophisticated, cultured, and respectable: like opera and classical music. Anything highbrow is usually intellectual in nature, and people who appreciate such things are also called highbrows. Highbrows usually have money and are sometimes considered snobby or hoity-toity. The opposite of highbrow is lowbrow, which refers to vulgar and less sophisticated culture and people. A book by a professor would probably be highbrow, while a book by a reality TV star is probably lowbrow.