'Oriental' used to be an official term for Asian people, seeing that they were people from the 'Orient'. It's out-of-date now though, and it follows the path of many pieces of out-dated academic lingo from being accepted social parlance to being recognised as offensive or derogatory because of the baggage they inherit from associated out-dated worldviews (words such as 'mongoloid', 'retard', etc.).
A note on offensiveness though, just because a person finds a term offensive doesn't mean it shouldn't be dropped. If it serves a specific purpose (and that purpose is not to offend), then largely speaking I think a person's offence should be ignored. I know that there is a small (or maybe large?) consensus that 'oriental' is somewhat offensive (or at least it is not politically correct), and that's maybe because it is modernly used to refer more to objects rather than people. This Asian friend, she took offence but it didn't seem that the person using the term meant any offence by it, in which case the Asian person's offence is fairly arbitrary. If a person doesn't mean to incite offence, then any offence felt is wholly incidental and so the person would do better to not allow their tranquility to be disturbed so easily, as if it were a house of cards.