Mai nafka minah is a colloquial, yeshivish question meaning "What's the practical difference?" It has no neat English equivalent. You might say "What's the nafka minah if she's Christian or Wyccan? The children still won't be Jewish" or "I still can't taste the nafka minah between Coke and Pepsi."
The Talmud frequently asks mai nafka minah (meaning literally "what goes out from it" in Aramaic) to identify the practical halachic consequences of abstract or theoretical arguments. For example, it gives three answers to the question of which biblical verse teaches us that a Succah may not be higher that 20 amot (about 30 feet.) A nice theoretical discussion; but then the Talmud wants to know what the nafka minah of the contrasting positions might be in terms of how a succah should be constructed.
The phrase embodies a characteristically talmudic sensibility; that thought, however abstract, should effect or express some practical consequence in the world.