A masu box is a square wooden box that was used to ration rice in Japan during the feudal period. Today masu boxes are smaller and used for drinking sake out of. If you came to my house I would put your cup into a masu box and pour till the sake overflowed into the box itself. This custom symbolises abundance, prosperity, goodwill and giving more than people expect; this is the essence of the Masu dining experience.
I would really like to take credit for the clever name, but I have to acknowledge Nigel Morrison as it was definitely a collaborative effort.