The literal translation is not "In what matter", but "In what is the matter" (дело is nomitative, not prepositional, so it is subject, not part of the "in"). Instead of asking "what" the matter is, or "where" the matter is, Russian asks "in what" it is: what is it, that "contains" the matter.
People should read the above comment because it is not just an excellent explanation of the meaning of this exercise, it also sets out a framework for interpreting a lot of other Russian sentences. This is an extremely useful bit of grammatical description/definition. I'm copying and pasting it into my study notes in red, so that I can find it easily.
I agree with GuidoSassi. "In what matter" or "In what business" should be an accepted translation. I will report it as a problem. As was mentioned above, and also in an earlier lesson in Duolingo, they translated "что не так" аs "what is wrong." So there is an alternate way of saying what is wrong.
"In what matter" or "In what business" has a different meaning than "What's the matter?" In what matter" would be каким образом или в каком деле; "in what business" would be в какой отрасле или в какой сфере. They don't mean the same thing as В чем дело which basically means "What's wrong".
Why the accusative rule for в (https://en.wikibooks.org/wiki/Russian/Grammar/Accusative_case) does not apply here? I.e. why is it "в чëм" instead of "в что"?
I have read all the previous comments and I am still confused. What is the intended meaning of В чём Дело.
-- "What is the matter?" as in What is wrong? (what the most common interpretation of the English sentence is) -- or "what is the matter at hand" as in What are we talking about? What is the agenda?" -- or something else?