Not a completely clear one, but "what for" is more precise than "why", which can be asking "for what purpose" or "due to what cause". "Why are you in my room" i

Not a completely clear one, but "what for" is more precise than "why", which can be asking "for what purpose" or "due to what cause". "Why are you in my room" is obviously asking the former, "why are the cookies burnt" fairly obviously the latter (unless you really did deliberately burn them to achieve some particular further goal...).