“they invited the people of Israel to the sacrifices of their gods.” The worship of the pagan gods involved ritual sex, as we see from Numbers 25:1. That was a major reason it was so attractive to the Israelite men. The verb “they invited” (more literally, “they called”) is a feminine plural verb, so it was the women who invited the men of Israel to the sex and sacrifice.
“and the people ate.” That is, they ate of the sacrifices that were offered to the pagan gods, thereby participating in the worship of those pagan gods, and they bowed down to them, that is gave them the reverence that should have been Yahweh’s alone.
“bowed down.” The common biblical way of bowing down before people or God was to fall to one’s knees and bow the upper body to the earth. It is the same Hebrew word as “worship.” [For more on bowing down, see commentary on 1 Chron. 29:20].