They show an image of it, it's that vertical abacus. They say it's popular in Japan. They have made a digital version of it, used a big keyboard as input, and gamified the practice. They also record how fast they can do calculations and stuff like this.

The point is for the author to understand how they learn (how many things become automatic in his brain and when, mental chunk formation, when performance plateaus). They just use the Japanese abacus as an excuse to do it.