The question mai nafka minnah is a way of testing the difference between two or more explanations for a given law, by investigating the different practical halachic rulings that would follow from each explanation.
It is contrasted with the question be-mai peligei, which also means "how do they differ", but implies that the two views have the same practical consequences and that the difference is the intellectual process by which they are arrived at (for example, which Biblical verse is the relevant authority).