Prim means polite, straight-laced, even twee. Many characters in Jane Austen novels are prim and proper.
Prim describes someone who is so concerned with being proper it becomes almost fake. If you go to the beach on spring break wearing a Victorian bathing costume, you're being prim. Clothes can be prim, too, like that long wool swimsuit. If you're feeling crazy, you can use prim as a verb meaning, "to purse your mouth into a prim expression" — like how you prim your lips when you look down your nose at someone using the wrong fork.