Plain weave is a fundamental weaving structure in which the weft travels over and then under adjacent warp ends. The weft does the opposite in the next row, traveling under/over a warp end it previously went over/under. Plain weave creates a smooth and strong cloth.
There are many types of weaving techniques that can be used to create different fabrics on multi-shaft and rigid heddle looms. This post has descriptions and photos of some of the most popular techniques.