Splay is a concave warp or curvature of a book's covers, curving away from the ends of the text block. Splayed covers occur more often than bowed covers. There are many causes of splay:
Stresses in the boards' directional grain can warp them.
A change in the boards' moisture content can cause their directional grain to warp in one direction.
Leather, vellum, cloth, or paper covering the boards can shrink more or less than the boards and warp them.
Pastedowns can shrink more or less than the boards and warp them.
The image shows two leather-bound press proofs from the Windmill Press, each copy being splayed.