The origin of the US Navy's Submarine Service Insignia dates back to 1923. On 13 June of that year, Captain Ernest J. King, USN, later to become Fleet Admiral and Chief of Naval Operations during WWII, and at that time Commander Submarine Division THREE, suggested to the Secretary of the Navy, via the old Bureau of Navigation, that a distinguishing device for qualified submariners be adopted. A Philadelphia firm, which had done work for the Navy previously, was approached with a request that it undertake the design of a suitable badge.
Two designs were submitted by the firm and these were combined into a single design that is still in use today: a bow view of a submarine proceeding on the surface with bow planes rigged for diving, flanked by dolphins in horizontal positions with their heads resting on the upper edge of the bow planes.
These Dolphins are the fish, also known as Dorado or Mahi Mahi, not the sea mammal many people are familiar with. They were chosen for the insignia because they are the mythical attendants to Poseidon.
The officer's insignia is a gold plated metal pin worn centered above the left breast pocket and above the ribbons or medals.
Enlisted men wore the insignia, embroidered in silk, in white on blue for dress blue clothing, and in blue on white for dress white clothing. This was sewn on the outside of the right sleeve, midway between the wrist and elbow. The device was two and three-quarters inches long. In mid-1947 the embroidered device shifted from the sleeve of the enlisted men's jumper to above the left breast pocket. Subsequently, silver metal dolphins were approved for enlisted men.
[Source: USSVI Dallas Base newsletter Up Scope Feb 2012]