In, from, or facing the southwest part of somewhere. It is an adjective, so it sits in front of a noun: the southwestern coast, a southwestern accent, southwestern France. Two things are worth separating. First, southwestern usually describes a REGION of a larger place — "southwestern Taiwan" means the bottom-left part of Taiwan, not a place to the southwest of Taiwan. If you mean a place lying outside and to the southwest, people normally say "southwest of Taiwan". Second, in American English "Southwestern" with a capital letter often means one specific region — Arizona, New Mexico, and nearby — and carries a whole flavour with it: desert, adobe houses, Mexican-influenced food, warm earth colours. A menu saying "Southwestern chicken" is promising you that style, not telling you a direction. In writing about weather and geography this word is everywhere; in casual conversation people usually just say "the southwest" and skip the adjective.