Gill pouches are the structures which are present in all vertebrates in the embryonic stages while it is present in fishes and amphibian in later life also.
It is thought to be the ancestral structures present in vertebrates. These pouches are then converted to lungs in the later life. For the water animals they are used for respiration.
They are actually the muscular walls containing respiratory lamellae on its inner side.
Hence in dolphin they are signs that dolphin is an vertebrate.
Dolphins having gill pouches would mean that dolphin embryos go through a fish phase during development. Dolphins are closely related so dolphins should go through a fish phase.
