Emily edited answer September 6, 2017
In the body of some organisms eg.birds (flight birds) air enters to the lungs and then into the air sacs. During expiration the air in lungs get out first and the air present in air sacs move into lungs and then comes out. Thus there occurs double respiration. Its significance is that it helps for flight birds to regulate their respiration during flight.
Emily approved September 6, 2017