Adverbials modify or tell us something about the sentence or the verb. It may be a single adverb, a phrase, or a prepositional phrase, or clause element.
When an adverbial modifies a verb, it changes the meaning of that verb.
The students looked at me.
The students looked at me anxiously. (The verb looked suddenly has a very different meaning).
When an adverbial modifies a sentence, the meaning of the sentence changes.
I passed all of my exams.
Surprisingly, I passed all of my exams.
Word groups that are also considered to be adverbials can also modify verbs: a prepositional phrase, a noun phrase, a finite clause or a non-finite clause.
Multi-word adverbials are sometimes called adverbial phrases.
I ran as quickly as I could, but I missed the bus.
If a whole clause acts as an adverbial, it's called an adverbial clause.
I'll go to bed when the film ends.