The small piece of soft tissue dangling over the tongue is the uvula.
It is variously described as U-shaped or tear-shaped, or classically speaking, grape-shaped; its name comes from the Latin word for grape.
While some anatomy experts think it is only a vestigial organ, not all would agree with your teacher that it has no function. Some might say that it helps keep grapes (or anything else) from going down your breathing passage when you swallow, and that is the action that many standard anatomy texts describe.
The uvula has its own little muscle, the musculus uvulae, to help it stiffen and change shape, so it helps fill in the space at the back of the throat.
Singers credit the uvula with letting them produce a vibrato, or wavy up-and-down sound, and the jazz star Anita O’Day says that her vibrato-less vocal style, using many separate notes instead, arose because she lost her uvula in a tonsillectomy.
The uvula is one of the soft-tissue structures that is often implicated in snoring and sleep apnea, or interrupted breathing during slumber. Some treatments for these conditions involve removing excess flesh from the uvula and surrounding areas.
The surgery, called uvulopalatopharyngoplasty, tightens up flabby tissues to enlarge the air passages.