An adverbial phrase usually consists of an adverb and one or more words either before it (premodification) or after it (postmodification) or, indeed, both.
The phrase performs exactly the same function in a sentence as it would if it were a single word. That is, it provides extra detail about how, why, when, where and in what manner the action of the verb occurs.
In the examples that follow, the adverbial phrases are in red; the words that modify the adverb are underlined.
We normally go to Spain in the summer.
Our holiday passes very quickly.
The Sun shone brightly enough.
The tapas were really good for the price.
Happily for us it did not rain.
We saved some of our money secretly to spend in the airport.
In line with adverbs, adverbial phrases can be of manner, place, time, duration, frequency, degree, certainty, necessity, evaluative, viewpoint or linking.