A phrase coined by some booksellers to denote that the copy was autographed in person, or that someone witnessed the book being signed.

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.

Flatsigned means the same thing as signed, thus, most books that have a standalone signature will simply be described as signed. Any further personalization will make the book inscribed.