| Definition -
Any optional word, phrase, or clause that modifies a verb or a verb phrase.
1. They are called adjuncts because they can be removed and the sentence remains well-formed.
2. If the adverbial is a necessary sentence element (i.e. you remove it and the sentence ceases to be well-formed), then it is an adverbial complement.
Example - Yesterday, Bob saw a zebra in the lane.
(Here yesterday and in the lane are adjuncts that modify the verb saw.)
Oxford English Dictionary - The term's first citation is from 1881:
"The basis and type of the Adverbial Adjunct is a substantive in an oblique case, used to limit or define the signification of a verb or adjective."
(Mason Eng. Gram. 149)