Adverbial phase.

In this very long compound-complex sentence, which I found it on a website, it explains that the underlined dependent clause is an adverbial clause:

“Thinking hurriedly about his words, the professor, given confidence by years of experience and energised by the anticipatory crowd, stepped onto the stage to make his guest appearance even though he wasn’t prepared to make a speech or deliver this lecture, which he’d spent barely five minutes rehearsing, to the audience of peers and students who sat eager-eyed, awaiting the first word that would soon leave his mouth.”

Can anyone explain to me why? What word or phrase does this adverbial phrase modify?

Thank you!