grammar - What does "an adverb tells us something about the sentence" mean?

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.