In this illusion, students take advantage of a (typically) unfamiliar sensation for our fingertips' touch receptors: having the skin on our fingertips stretched.
When we place our fingertips against a brush-like surface with semi-rigid bristles, and then move the bristles back and forth, the skin on our fingertips becomes alternately stretched and compressed by the undulating motions. Because of the novelty of this particular sensation, our touch receptors have difficulty interpreting it properly. Instead, we reinterpret the stretch/compress motion as the more familiar sensation of running our finger across a raised surface, like a dot.