If you read further down the page in the Wikipedia article where you found your example, you'll find how adverbials modify sentences:
Types of adverbials that form sentence elements
Adverbials are typically divided into four classes:
adverbial complements (i.e. obligatory adverbial) are adverbials that render a sentence ungrammatical and meaningless if removed.
John put the flowers in a vase.
adjuncts: these are part of the core meaning of the sentence, but if omitted still leave a meaningful sentence.
John helped me with my homework.
conjuncts: these link two sentences together.
John helped so I was, therefore, able to do my homework.
disjuncts: these make comments on the meaning of the rest of the sentence.
Surprisingly, he passed all of his exams.