"Oriental" is generally considered old-fashioned now, and many find it offensive. "Asian" is preferred, but not "Asiatic." It's better to write the nationality involved, for example "Chinese" or "Indian," if you know it. "Asian" is often taken to mean exclusively "East Asian," which irritates South Asian and Central Asian people.
Wikipedia explains the origin of the term:
The term is derived from the Latin word oriens, which is the present participle of "orior": to rise. The implication is the rising sun, hence the use of orient to describe the "land of the rising sun", i.e. the Far East. The opposite term "Occident" -- derived from the Latin word occidens, from the verb "occido": I fall -- was once used to describe the western world, i.e. the "land of the falling (setting) sun", but has, coincidentally, fallen into disuse.