Translation:What are your relations with this man?
"Relacje z tym czlowiekiem" means 'relations >with< this man'. "Relationship" means 'związek' in polish, something more personal, like realtionship >between< a boy and a girl (a couple). "What is your relationship with this man?" could be translated to 'Jaki masz związek z tym człowiekem?' or 'Co cię łączy z tym człowiekiem?' - it is also accepted, but for me it's not so natural :)
I have read the comments below and can only add that in English the sentence does not really mean anything as it stands. If we were to ask how well we know someone, or whether we get on well with them I think we would ask those questions. Otherwise we might just say " What is your relationship like with this person". But I do understand your comments already made.
What are your relations with this man?
That doesn't make sense in English. Poles often mix relation and relationship up. Perhaps it should be:
What kind of relationship do you have with this man?
How are you related to this man?
Also, you may want to be careful using "relations." It reminds me of Bill Clinton. "To have relations" is VERY different than "To have a relationship," with the former being sexual and the latter ambiguous.
What is your point, Miĥal? I know the definition. Relation might be used this way in Appalachian (and therefore perhaps Scottish) English, but in standard American English it doesn't work.
How about "What is your relation to this man?" That mostly keeps the same sentence structure as the Polish.