Many phrases can act as adverbs and modify a verb, another adverb, or an adjective. A prepositional phrase can act as an adverb and modify a verb: In May, it often rains. A verbal phrase can act as an adverb: To scare the intruder, the homeowner brandished his gun.
Strictly, an adverbial phrase is a group of words having an adverb as the first word. We can build far more adjectival phrases (free from bias, pertinent to our case) than adverbial phrases. Here is an adverbial phrase:
Oddly enough, the defendant admitted his guilt.