What exactly does to the third and fourth generation mean?

The phrase “fourth generation” has idiomatic value, as in the phrase “punishing . . . to the [third and] fourth generation” (Ex 20:5, 34:7; Num 14:18; Deut 5:9). In this context it refers to the entire household, with the four generations being the patriarch, his children, his grandchildren, and his great-grandchildren, all of whom would live together as an extended family (bét-’ab, lit. “father’s house”).— The Lost World of the Israelite Conquest, 59