SVA : She was there. SVOA : She put the book on the table. (source)
Is the Adverbial [of CGEL’s clause types] that is necessary in a sentence called because it modifies verb; or because it has the certain semantic meaning, like time, space, etc?

SVA : She was there. SVOA : She put the book on the table. (source)
Is the Adverbial [of CGEL’s clause types] that is necessary in a sentence called because it modifies verb; or because it has the certain semantic meaning, like time, space, etc?

They use adverbial to mean an adverb (e.g. there) or a group of words that works as adverb (e.g. "on the table" in "She put the book on the table."), which is normally called adverbial phrase.