An officer who gives parking tickets. A parking meter is a type of clock that you put money into and it allows you to park for a limited time.

Phil's answer below is correct. Note that the word isn't "metre" (which is a unit of measurement) but "meter" (which is a machine that measures the use of something—time and distance in a taxi, water in a home, etc.). Regarding your joke, a meter man would be a very low-level policeman, someone who wasn't qualified to be a "real" police officer; therefore, the senior officer is threatening the other man with a demotion for asking stupid questions. In fact, in the past it was a job assigned to women ("meter maid") because police departments didn't believe a woman could do the job of a police officer (obviously, and happily, this has changed!).