A dust jacket is the printed paper wrapper that folds around a hardback's boards. It began as plain protection but became the book's advertising, carrying the cover art, blurbs, author photograph and price, and for most modern collectable books it carries much of the value too.
How to spot it
A jacket has a front panel, spine and rear panel, with flaps that tuck inside the boards. Check that the jacket belongs to the book: the price, publisher and reviews should match the edition and date, and the size should fit. Later jackets were sometimes put on earlier books, which collectors call a married copy. Look at condition separately from the book: chips at the spine ends, tears, rubbing, fading of the spine and clipped prices are the usual faults.
What it does to value
For twentieth century first editions, a book without its jacket is often worth only a small fraction of a jacketed copy, and the jacket's condition moves the price as much as the book's. That is why book and jacket are graded separately. Facsimile jackets, modern reproductions of the original, are worth very little in themselves and must be described as such.
See dust jackets explained, facsimile dust jackets and book condition grading.