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.

For example:-

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.

For example:-

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.

For example:-

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.

For example:-

I'll go to bed when the film ends.