Peristalsis is most commonly used to refer to rhythmic smooth-muscle contractions that provide motility in the digestive tract. This type of rhythmic contraction is the basis of a class of pumps -- peristaltic pumps -- that move fluids through tubes without direct contact with pump components. This is a particular advantage in biological/medical applications where sterility is of utmost importance, as the pumped material need not contact any surface except the interior of the tube.
The peristaltic pump demonstrated uses a rotating hexagonal bearing sandwich (om nom nom!) in which the tube is pinched by the bearings against a concave thing. Three bearings contact the tube at any given time, so the fluid in the tube is moved as the rollers move. This creates lower pressure at the inlet, and higher pressure at the outlet, so the fluid moves.