Inscribed
When a book is described as being inscribed, it indicates that a short note written by the author or a previous owner has been written in the book (usually on the ffep or front pastedown) and is generally accompanied by a signature.
An inscribed book can be categorized in three ways.
A book that has an inscription that is neither to or from the author (or a person of historical interest) has no additional collectible value. In fact, this will generally detract from the collectibility of a book. An example might be an inscription that reads, "To my lovely niece Mabelline on her 16 birthday. Love, Aunt Isabelle." Of course, to Mabelline or Aunt Isabelle or later family, this may be priceless, but on the collectible book market, it tends to diminish the value.
A book that has an inscription from the author (or a person of historical interest) to someone who is not still retains enhanced collectibility. For example, if Cormac McCarthy were to inscribe a book to "Dear Dan, best of luck, Cormac McCarthy", this likely has less collectible interest than a book that simply had McCarthy's signature. (Unless, of course, you are Dan). That said, it still does have additional value over an unsigned book (especially in McCarthy's case; owing to his reclusiveness, his signature is considered very collectible).
A book that has an inscription from the author (or, again, a person of historical interest) to someone else who is of some note or relevance is called an association copy, and is typically valued very highly.