A price-clipped jacket has had a small corner cut from the front flap, where the publisher printed the price. Booksellers and gift givers did it for decades so the recipient would not see what the book cost, which is why so many otherwise fine jackets turn up with a missing triangle.
How to spot it
Open the front flap and look at the top or bottom corner. A diagonal cut, often neat and sometimes ragged, means the price has gone. On some books the price sat on the back flap or the rear panel instead, so check the publisher's usual position before deciding. A jacket with a price sticker over the printed price is not clipped, though the sticker can damage the paper if removed.
What it does to value
Collectors treat clipping as a fault, because the printed price is one of the ways to date a jacket and to tell a first issue from a later one. A clipped jacket on an important first edition is typically worth noticeably less than an unclipped one in the same condition, and the gap widens at the top of the market. It matters most when the price itself is a point of issue, for example where later jackets carried a higher price.
Dealers always mention clipping in a description, so an unmentioned clip is grounds to return a book. See dust jackets explained for how prices date a jacket, and book condition grading for how faults are described.