When a fabric is woven, its fibers are interlaced in a crisscross pattern, horizontally and vertically. Think of weaving strips of paper together in grade school, when you’d interlace the paper to create one big woven swath of paper. Woven fabric is the same way. Because of this weaving method, woven fabric tends to hold its shape better and doesn’t really stretch. This can be helpful when trying to keep things precise while sewing and perfectly even and straight. So, cutting along the grain of the fabric, means cutting parallel to the woven fibers of the fabric.