The students began whispering and giggling once they saw the teacher close the book, The adverb clause once they saw the teacher close the book modifies what?

This adverb clause modifies the verb phrase began whispering and giggling, by telling when the action happened. An adverb clause is a dependent (subordinate) clause, which means that it cannot stand on its own. If it stood on its own, it would be an incomplete sentence. Therefore, it is a supplement to the main clause. In this case, it begins with a subordinate conjunction once.