During Musaf, it is customary to bow down at various points during the description of the Yom Kippur avoda (Temple service), just as the kohanim and the spectators in the Temple courtyard bowed and fell to the ground when the Kohen Gadol uttered the Tetragrammaton. As we will see (10:15-16), the Kohen Gadol uttered it ten times: nine of them in the course of three confessions, and the final one when he announced which goat was for God. The three confessions were on behalf of himself and his wife, on behalf of his fellow priests, and on behalf of the nation. Nowadays, the general custom is to bow four times during the prayer service. We bow once during the descriptions of each of the three confessions. The timing of the fourth bow, however, is the subject of dispute. Sephardim bow when they mention the goat for God (Beit Yosef; see 10:9 below). Ashkenazim bow when reciting “we bow” (“va-anaḥnu kor’im”) in Aleinu, preceding the description of the Kohen Gadol’s avoda (Raavya; Rivash; Rema 622:4). Yemenites do not bow at all during Musaf.
There are three types of bows: prostration (hishtaḥavaya gemura), in which a person lies flat on the ground with hands and feet outspread; kida, a deep bow in which a person remains standing but bows his head all the way to the ground; and keri’a, when one first kneels and then bends forward until his face reaches the ground (Berakhot 34b; Shevu’ot 16b). Nowadays, most people do keri’a, while some do hishtaḥavaya.
It is customary to place something on the ground as a barrier between the floor and the worshipper’s face. This is because it is forbidden to bow on a stone floor, as we read, “You shall not place figured stones in your land to worship upon” (Vayikra 26:1). The reason for the prohibition may be that idolaters would worship nature and bow to stones in an attempt to become one with them. The Torah forbids bowing on stone so that no alien ideas infiltrate our prayers. Only in the Temple, where it was clear that all creations – animate and inanimate – were subservient to God, yearned for Him, and bowed to Him alone, was it permitted to bow on a stone floor (Sefer Ha-ḥinukh §349).
The Torah prohibition applies when two conditions are met: the person is lying prostrate, and his head is on a stone floor. The Sages extend the prohibition and forbid bowing when either one of these conditions is met. Thus, hishtaḥavaya is prohibited even on a dirt floor, and even kida and keri’a are forbidden on a stone floor. For this reason, people spread something as a barrier between the floor and their heads (Rema 131:8).
If the flooring is made of a material other than stone, even if it looks like stone, all agree that one may put down a separation and then prostrate himself.