The Ziggurat (ジッグラト jiggurato?) is an alternate layer of reality where Hand Shakers battle. To be able to access it directly is to become a Hand Shaker. Once a hand shaker pair lost they will be unable to stand within the Ziggurat. Another way to be kicked out is if you are 1000 ft away from the general battle area as stated by Makihara.
The Ziggurat is mainly the same as the normal world except that it has vast colors and designs upon one another and any damage done there will not be reflected on the real world.