Have you ever tried to tear a piece of paper and notice that it tears better in one direction compared to the other? Why is this?
The way paper tears is related directly to how it is made. Most paper is made from wood fibers. Logs are chopped into wood chips, mixed with water and chemicals, and run through a process that separates the wood fibers. The soupy mush that results is called pulp. The pulp is pressed onto a mesh conveyor belt that squeezes the water out.
As the pulp moves along the belt the wood fibers line up in the direction of the belt's travel. This alignment of the fibers on the belt gives the paper a grain.
This grain is what causes the paper to tear straighter one way than the other. When paper is ripped with the grain the tear goes with the direction of the fibers, and is fairly straight.
When you tear the paper across the grain the tear tends to wander as it works against the direction of the fibers.