A "naval destroyer" is a warship. "Naval" is a homophone of "navel". The navel is the place on a person's belly where the umbilical cord detached after birth. When the belly button gets pierced, the skin experiences trauma, maybe even gets a bit destroyed, and has to heal around the piercing. The sailor's girlfriend has a belly ring. This is where "navel destroyer" makes sense. This joke is playing on the term "naval destroyer" because it sounds like "navel destroyer". 
The sailor called his girlfriend ' s belly ring a naval destroyer .