What does SS mean in a US Navy rate?

"SS" is a warfare specialty designator, signifying a sailor is "Qualified in Submarines". The "SS" itself stands for "Submersible Ships", not "submarine sailor" as many people incorrectly assume.

"SS" designation also comes with its own warfare insignia pin, worn as silver (enlisted) or gold (officer) dolphins abreast the bow of a submarine.

Submarine qualification takes most sailors about 8-12 months, depending on their particular rate and workload aboard ship. Nuclear rates typically take less time, since part of their nuclear training is at a shore station nuclear power plant that is similar to a shipboard reactor.

Unlike other warfare designators (Surface, Aviation), it is mandatory for all submarine crewmembers, be it the lowest ranking sailor or the Captain, to qualify in submarines. Qualification is heavily weighted toward damage control during a casualty.

The rate designation is added at the end of the rate; e.g., my old rate designator was STS1(SS), which fully written out would be "Sonar Technician(Submarines) First Class (Submersible Ships).