What is a subordinate adverbial clause?

Grammatically, subordinate adverbial clauses function within sentences as adverbs. Just as most adjective clauses begin with a relative pronoun, adverb clauses always begin with a subordinating conjunction (after, before, unless, although, when, while, as soon as, as long as, as if, where etc) marking them as grammatically subordinate.

They have subjects and verbs and sometimes objects. The adverb clause does not express a complete thought. Adverb clauses function to modify verbs, adjectives, or another adverbs.

Examples:

The whole country was saddened when Oswald assassinated Kennedy.
(when Oswald assassinated Kennedy => subordinate adverbial clause)

Although Spike broke the window, he did not feel guilty about it.
(Although Spike broke the window => subordinate adverbial clause)

Since Grandfather died, I have been lonely.
(Since Grandfather died => subordinate adverbial clause)

I wouldn't mind getting out of bed, if only I didn't have to go to work.
(if only I didn't have to go to work => subordinate adverbial clause)

Hope it helps