A flatsigned book is signed, and not inscribed, directly on a page of the book, rather than on a bookplate or with an accompanying inscription. The term is generally attributed to Stephen King who appears to have coined it in 2000.
Typically a book that is signed without an accompanying inscription is a more collectible copy than an inscribed book (association copies notwithstanding).
While commonly used to describe a standalone signature in a book, many dealers still shy away from using the term, perhaps owing to its pop culture roots. Thus, many books that have a standalone signature may not employ the term flatsigned in describing them.