to bring a child into the world: of a father, to father a child; of a mother, to give birth; of a child, to be born
This is the ordinary word for the start of a human life, and Greek lets one verb cover every side of it. Used of the father, it describes his part, the line of descent that the genealogies trace name by name. Used of the child or mother, it shifts to the child simply being born, or to the mother's labor of giving birth.
Because the same verb runs through a whole family tree, it carries the sense of a chain: each person fathers the next, and the New Testament uses it to anchor real people in real history, from Abraham down to Jesus. The shape the verb takes is what tells you whether the focus is the parent who produces the child or the child who is produced.