The grain direction of a textured sheet of paper is fairly obvious, but all paper has a grain whether you can see it or not. Grain is created in the paper making process; the fibers used in raw pulp are poured over a continuously moving fine mesh belt. The water is drained and pressed out of the pulp, and the moving belt causes the fibers to line up in the direction of the motion.
Paper that is “grain long” has the grain running along the long dimension of the sheet, so the grain of a “grain long” 8.5 x 11 sheet runs along the 11” dimension. To determine the direction of the grain, hold both sides of the sheet together so the middle curves. Press lightly on the arc of the curve. Then turn the paper 90 degrees and do the same. There is more resistance when the sheet is running against the grain. Paper can bow or buckle along the grain as it is heated and dried during the printing process. Climatizing paper before printing and re-hydrating the paper after printing can help.
Grain can make a big difference in printability and binding. Since paper has less resistance to being folded along the grain than against the grain, it is an important consideration when a printing job is folded.
Heavy paper stock can crack when folded against the grain, and scoring or other special treatment may be needed to avoid objectionable cracks. If a strong bind is important, it can be a good thing to fold against the grain, but because paper can bow and curl along the direction of the grain, folding against the grain may make the finished product lay less flat.
Economics is also a factor to consider. The most efficient cut may not leave the sheet in the proper orientation for printing and binding, so the printer and designer strike a balance between design, printability and price.