It means fifteen years of service, as Peachy noted. It is very likely that naval ranks and careers follow some understood ladder, and expectations of achieving certain ranks after certain numbers of years of service. Someone who has not been promoted to rank X after Y years is not likely to be promoted further at all... things like that. Very likely fifteen years of service is understood to be some important turning point. The number of years of service is very important in a military career, because if two officers have the same title (e.g. "commander,"), the one with more years of service outranks the other.

I think it's self-explanatory: fifteen years of service in the navy.