What does Ruth 4:16 mean?

Naomi left Bethlehem with a husband and two sons. She returned with a Moabite daughter-in-law. She told her old friends, "I went away full, and the LORD has brought me back empty. Why call me Naomi, when the LORD has testified against me and the Almighty has brought calamity upon me?" (Ruth 1:21).

That grief will stay with her forever. No one can suffer that much loss and simply get over it. What she no longer must carry is the shame of not providing a male heir for her husband and the fear that no one will care for her as she grows old. She can also let go of the belief that the God of Israel has abandoned her. It was Yahweh who lifted the famine in Israel and drew Ruth to follow her to Bethlehem (Ruth 1:6, 16–17). And Yahweh allowed Ruth to get pregnant with a son on Naomi's behalf (Ruth 4:13).

"Nurse" in Hebrew is 'aman and can also mean foster-parent. The same term describes Mordecai with respect to Esther (Esther 2:7). This has led scholars to suggest Naomi kept Obed at her home and raised him, herself, while Ruth lived with Boaz. That's possible, but the text doesn't say so directly.

"Lap" is mistranslated. It occurs in Proverbs 5:20 and Lamentations 2:12 correctly as "bosom" or "breast." An alternate form is translated "embrace." Naomi was Obed's wetnurse; she literally breastfed him.