An adverb is a word used to modify a verb, an adjective, or another adverb. Other sentence elements such as phrases and entire clauses may function as adverbs. Any element that functions as an adverb is an adverbial, but sometimes all adverbials are simply referred to as adverbs without regard for the distinction between individual adverbs and adverbial phrases and clauses. Adverbs provide context as to how, when, where, and to what degree something is so.
John decisively won the match.
The adverb decisively modifies the verb won to describe how John won.
Selena jogged to the park.
The prepositional phrase to the park functions as an adverb modifying jogged to tell where Selena jogged.
The sweater was old and extremely ugly.
Extremely modifies the adjective ugly to describe an extreme degree of ugliness.
Roger drove to the store yesterday.
Drove is modified by two adverbials. The prepositional phrase to the store tells where Roger drove, and the adverb yesterday tells when he drove to the store.
Grace usually does her cleaning on Saturday.
The adverb usually modifies does to describe how often Grace does her cleaning, while the prepositional phrase on Saturday describes when she does her cleaning.
Jordan acted as if nothing had ever happened.
In this sentence, an entire dependent clause modifies acted to describe how Jordan acted.
Adverbials come in many shapes and sizes serving many different purposes. Simple common adverbs may be easy to spot, but adverbial phrases and clauses are often more difficult to figure out. As always, it is best to find verbs and their subjects first before trying to figure out how other elements are functioning in a sentence.