An inscribed book carries a handwritten message from the author as well as a signature, usually addressed to a named person: "For Margaret, with love", for example. It differs from a signed copy, which carries the signature alone.
How to spot it
Inscriptions usually sit on the front free endpaper, the half-title or the title page. Check the hand against known examples of the author's writing, and look for the date and place, which can help confirm when it was written. A printed facsimile signature, common on some special editions, is not an inscription. Book plates signed by the author and pasted in are described as signed bookplates.
What it does to value
Collectors differ on inscriptions. Many prefer a plain signature, or a signature with a date, to an inscription to an unknown person. An inscription to someone significant, which makes the copy an association copy, can add a great deal. An inscription to a stranger adds less than you might expect, but it is still worth more than an unsigned copy.
See signed and inscribed books for how to judge a signature and how different kinds compare in value.