The damaged book is a book held in the pocket slot that can be obtained for 5,000 coins from Jossik after completing Horror From The Deep. The four Zamorak pages can be added to upgrade it to Zamorak's Book of Chaos, which gives a damage bonus. Dropping or destroying a damaged book and talking to Jossik results in him returning the book.
Players can check which pages are currently in your incomplete book with the "Check" option. Filling the book with all pages currently costs 759,123 coins. Once a page has been placed in a book, it cannot be removed.