Aux. is a written short form of auxiliary, and in grammar books it often means auxiliary verb — the little helping verb that stands with the main verb, like be, do, have, will, or can. You see aux. in dictionary lines, in school grammar notes, and in older labels (aux. nurse, aux. engine). People almost never say “aux” out loud for this grammar use; they say auxiliary or helping verb. Though actually, the same three letters show up in other places, so the letters alone do not tell you which meaning you have. In this entry it is the grammar / helping-word label. In a Taiwan classroom, if your teacher writes aux., they almost always mean the helping verb. It is a mark on the page, not a word you need to pronounce in a sentence.