If you are describing the cushions that Buddhists use for meditation, the round cushion that is sat upon is called a Zafu in Chinese / Japanese. The rectangular cushion that the Zafu is sometimes placed upon is called Zabuton in Japanese.
Sitting meditation. The principal practice of Zen Buddhism.The typical sitting mode involves a small round cushion (zafu) and a square mat (zabuton). You place the cushion on the mat and sit on the cushion with your legs crossed--lotus position if you can, or some variant if you can't.There's a prescribed posture (very straight, but not rigid), hand position, and direction of gaze.You sit very, very still for a prescribed sitting period (such as 40 minutes), focusing on your breathing and not on your thoughts.
One of the features of Japanese traditional house is the floor is covered with straw mats (tatami) and the other feature is it use sliding door (shoji screen).Many traditional houses have a small area (a bit like a shrine) to pray to ancestors and to God.