Jersey cotton is made out of 95% cotton and 5% of this elastic stuff, an easy way to explain it is it's like a spandex material.
Zig Zag stitch is the main stitch that is used on stretchy material. The reason for that is because it’s a lot easier to sew and holds very well together.
Jersey cotton is normally made using stocking stitch but can also be made out of rib stitch or pattern that are knitted in.
With the process of making jersey cotton is usually made with a normal sewing or a weaving sewing machine because the fabric is to delicate and complex to hand stitch and/or sew.