A stickler is someone who insists that things are done in a certain way. Say you’re getting married and want to write your own vows, but your partner’s mother demands that you have a traditional ceremony. The mother is a stickler for tradition.
Stickler has its origins in a word meaning umpire, which may allude to a stickler’s bossy nature. Difficult problems or puzzles are called sticklers. It is helpful when remembering the definition of stickler that it has the word “stick” in it. So someone who “sticks” to the rules is a stickler.