A semi-auxiliary verb is a two-part or three-part verb beginning with “be” or “have.”

Semi-auxiliaries include be about to, be able to, be going to, be likely to, be supposed to, had better, have to, ought to, used to, and would rather. Here are some examples of sentences that include semi-auxiliary verbs in them:

I am able to do 200 push-ups. They will be able to do 200 push-ups.

He was about to tell me his secret before you interrupted. He is likely to remain silent, now.

You had better not interrupt again. You are supposed to be just an observer here.

I would rather you were not here at all. I’d rather you didn’t participate in this discussion.

Note: semi-auxiliaries seem similar (but are not quite the same as) phrasal auxiliary verbs.