An auxiliary verb is a verb used in conjunction with a main verb to form tenses, questions and negatives. In English, the primary auxiliary verbs are do, be, and have: Do you like coffee? You are working hard. I haven't been there.
These three verbs can also act as main verbs.
The full name for modal verbs is 'modal auxiliary verbs.' They operate in the same way though the meanings they convey are different.