This video shows a young Green Frog (scientific name Rana clamitans or Lithobates clamitans) shedding its skin and eating it. The frog repeats the same cycle of behavior. First, it rotates its hind limb, then it rotates its front limb, and finally it opens & closes its mouth. The roll of shedding skin is visible between the frogs front and hind legs.
Why do frogs eat their shed skin? I am not aware of any experiments that investigate the benefits of eating skin in amphibians. Perhaps there is some nutritional benefit to eating the skin?