Adverb Clauses are clauses that function as adverbs (they modify verbs, adjectives, and adverbs). They are often introduced by subordinate conjunctions: when, where, as, than, whenever, after, if, while.
Examples:
1. When they arrive, show the guests to their seats. (notice the comma after the introductory adverb clause).
2. Put the flowers where everyone can see them.
3. His brother is late as he is.
4. Your serving of ice cream is bigger than mine (is). (often, the verb is omitted).
5. You should visit whenever you can.
6. After he fumbled with the words for a minute, John finally proposed to Jane.
7. If you are going to argue, you can stay home.
8. While the rest of the city sleeps, the garbage men work.
Notice: often these subordinating conjunctions are simply adverbs. Remember that clauses need verbs to exist (NOT gerunds or participles… verbs!).
Examples using after:
1. After dinner we went to the movies. (simple prepositional phrase).
2. After working on the project all evening, the student collapsed in bed. (again, a prepositional phrase. The gerund working on the project all evening is the object of the preposition after.)
3. After he worked on the project all evening, the student collapsed in bed. (here, worked is a verb, and, thus, after he worked on the project all evening is an adverb clause.
(See more examples in The Writing Guide "Using Clauses" Section)