분수를 알라는 말이 괜히 나왔겠습니까?
= Would the saying 'know your place' have been coined for no reason?
= It is not for no reason that they say 'Know your place'.
분수 is the traditional concept of one's station in life, limitations, etc. and 분수를 알다 means knowing one's bounds and acting accordingly. For instance, a kid from a modest family shouldn't try to behave the same way as kids from billionaire families.
분수를 알라는 is short for the reported speech from 분수를 알라고 하는, which is the same as '분수를 알아'라고 말하는 (telling you/someone to know your place). So 분수를 알라는 말 is 'a saying telling us to know our place'.
Other examples: 정지하라는 명령 = an order (telling me) to halt / stop, 벌금을 납부하라는 통지서 = a notice (telling me) to pay the fine.