Title basically says most of it. To add more context to that 「YOUは何しに日本へ？」 is a name of a japanese TV show, found it on YouTube. They meet random foreigners at the airport and ask them this question. I can make an intelligent guess that this is contacted form of 「何するのに」, but I have doubts, since why would they ask a question with slangy words to people who can hardly speak the language? On the other hand the use of 「YOUは」 might indicate that this whole phrase can be slangy from the start. Many thanks.
[Verb Stem]に行く or に来る, such as 試しに来た (I came here to try it), means to come or go for the purpose of doing the verb.
Xしに来る is a common usage which applies this for Xする verbs.
So「YOUは何しに日本へ？」 is short for 「Youは何をしに日本へ来た？」, meaning "what did you come to japan to do", or perhaps more fluidly and less literally, "what did you come to japan for?"