grain direction
OAB Definition
according to common understanding, grain direction is the predominant directional alignment of cellulose fibers in a sheet of paper. Grain direction is determined by the papermaking process. In a finished sheet, fibers swell as they absorb moisture, which causes the sheet to expand primarily perpendicular to the direction of the grain. Folding and tearing is also easier along the same axis as the grain.

Paper dampened on one side will curl perpendicular to its grain direction.
When making books, understanding grain is important in that the grain direction of all materials should run parallel to the spine so that materials expand and contract primarily in the same direction when adhered to one another with wet glue. Also, the drape of a page is more pleasing when the grain is parallel to the spine, rather than the stiff page that results when the grain is perpendicular to the spine.
According to research by Richard P. Grant grain direction is both predominant fiber direction and a result of paper drying under constraint, particularly when the constraint is in one direction. The unconstrained dimension shrinks during the paper making process, creating very small wrinkles or ridges which are more easily folded and torn along. When the paper is dampened, those ridges smooth out, expanding the paper in the unconstrained dimension.
Images used with permission from Skin Deep, a publication of J. Hewit & Sons Ltd. OAB expresses gratitude to Daniel Kelm for sharing this resource.