What do leather, paper, and felt have in common? Fibers matter!
Grain in leather is the outermost layer. Grain can also refer to the fibers themselves as in grain direction. The direction across the grain is going to be stronger as a force would have to cross all the fibers. Folds should be parallel with the grain direction to prevent cracking. The longer fibers will bend away from each other to stretch, and stretching is not going to be desirable in straps like watchbands and belts. In the torn paper image above, one direction that I tore it in was quite straight as it followed down the grain fibers. The 90 degree tear zags back and forth.
Felting tangles up the fibers. This resembles the looser fibers in a split or suede leather. Hand pressed papers will also have a less consistent grain structure. The thing to remember about these is that they will be more prone to stretching or being pulled apart.