“Auxiliary (Aux): A verb belonging to a small class which syntactically accompanies other verbs: distinguished as such from a lexical verb, of full verb. E.g. could and have are auxiliaries, accompanying a form of write, in He could have written it. The first belongs to a class of modal verbs that can stand alone, as in a sentence I could, only if a following verb is ‘understood.’ The second is an auxiliary related to the past participle (written); distinguished accordingly from have as a lexical verb, e.g. in I have the answer.
Auxiliaries usually mark modality, tense, or aspect: e.g. the construction of have with a past participle marks the perfect. Hence the same term has been applied to other grammatical words that mark such categories, whether or not they are verbs.”
Excerpted from: Matthews, P.H., ed. The Oxford Concise Dictionary of Linguistics. New York: Oxford University Press, 2014.