It is a pattern consisting of crossed horizontal and vertical bands in two or more colors in woven cloth. The reason why the pattern is called koshi is because it looks like a wooden frame designed in a grid (koshi) used for a shoji screen or a door.
Sometimes, we call it a check pattern in Western style. The koshi pattern composed of big squares is called “Ogoshi” and the one composed of small squares is called “Kogoshi.”
The koshi pattern became popular among the kabuki actors in the Edo period and then it gradually became popular among the ordinary people.