Two closely related uses. As a noun, an occidental is someone from the western part of the world — Europe or the Americas, on that old East/West map. As an adjective, it means “western” in the same cultural-geographic sense: occidental art, occidental medicine. It is formal, a little old-fashioned, and more at home in essays than in the street. People usually just say “Western” or “a Westerner.” Though actually, calling a person “an occidental” can sound as if you are sorting humans into East and West, which many people now find clumsy or dated; the adjective still turns up in academic writing.