The subdermal sheath attaches some of the dolphin's muscles to its skeleton and provides some of the "spring" in the animal's movements.
—Adam Summers and Sally Bensusen University of California

As swimming muscles lift the dolphin's tail, blubber on the top side is compressed while blubber and the fibers of the subdermal sheath on the bottom are stretched, storing energy for the downstroke.

As the muscles relax, the previously compressed blubber springs back and may help push the tail down. The now compressed blubber and sheath on the tail's underside may also contribute to the downward pull on the tail.

Adam Summers and Sally J. Bensusen – University of California