A guest book is used to gather info on the people who stayed at the hotel, or paid their respects at a funeral, etc. You send a thank you note, in appreciation of them visiting. In business cases, it helps also, in keeping track of the amount of guests per month, season, etc.
A guestbook is a book or paper that visitors or guests sign in order to ensure their visitation to a certain area or site. It's very hard to tell why people might avoid signing a guest-book; as there can be many reasons.