Originally the word was a corruption of purser, used to refer to that person (the paymaster on ships of old, and presumably new ones too). Somewhere along the line it became used to refer to the Navy as a whole, and anything related to it.

Hence the following constructions:

• Pusser's Rum (an actual brand name)
• Pusser's red -- military-issue bicycle, often red in colour
• Pusser's dirk -- sailor's knife (a jackknife, ahahahahahahaha)
• Pusser's tan -- the kind of forearms-only suntan you get when wearing a uniform shirt
• and many many more!