“Boh” is a strange and unique Italian interjection used to express uncertainty. It is the equivalent of saying “I have no idea” or “I have no clue” in English. This expression is often accompanied by wide eyes and a shoulder shrug.
So if someone asks you something that you do not know the answer to, you can respond by saying “boh”. However, you should not reply “boh” to just anyone. The term is very informal, so you should not say it to professors, for example. However, the response would be appropriate for close friends.