What does Ruth 3:10 mean?
On what is likely the final night of a prosperous harvest, as the workers sleep on the threshing floor, protecting the newly winnowed grain, Boaz awakens to see a figure lying at his feet. It's Ruth, and she has a proposition (Ruth 3:1–9). Boaz is a good man—and rich. He's also related to Ruth's late father-in-law. That means Boaz can buy Elimelech's land, thus providing for his widow's needs (Leviticus 25:25–28, 47–49). In addition, Ruth challenges Boaz to marry her and provide an heir for Naomi who will re-inherit the land to keep it in Elimelech's family (Deuteronomy 25:5–6).Naomi told Ruth to proposition Boaz for Ruth's sake—so she would have a good husband and find "rest" (Ruth 3:1). Ruth has spent two months gleaning from Boaz's fields. At least half of Boaz's harvesters are young men—closer to Ruth's age. She could have presented herself as available to any of them. She didn't, however. Only the older Boaz can give her what she really wants.
Many Bible scholars have interpreted Boaz's words to mean he appreciates that Ruth, a young vibrant woman, has chosen him, an old codger, as if he needed his ego stroked. That's not the "kindness" Boaz is referring to. The first "kindness" was when Ruth left her family and her homeland and traveled from Moab to Bethlehem to take care of Naomi—something Boaz has already praised her for (Ruth 2:11–12). Now, Ruth goes above even that kindness. She could have found herself a rich young man or a poor man she loved; either would have been around for a long time and given her lots of babies. Instead, she wants to marry a relative of her in-laws. She chooses family loyalty over her own self interests.
Levirate marriages are part of the Mosaic law. If a man dies with no heirs, his brother is to marry his widow and have a son in the dead man's name. The son will receive the inheritance of the dead man. This is the story of Tamar (Genesis 38) and one part of the Sadducees' argument against the resurrection of the dead (Mark 12:18–27). Naomi is bitter not just for herself, but because when her sons died, she failed in providing Elimelech an heir (Ruth 1:1–5, 20–21).
Boaz doesn't meet the literal interpretation of the law: he is neither Elimelech's nor Ruth's late husband's brother; he's a more distant relation. But he sees that Ruth is willing to give up her life and her future for Naomi's honor. In response to her continued kindness, the least he can do is marry this young, honorable, loyal, hard-working widow!
"Gone after" often describes either illicit sexual relations (Proverbs 7:22; Hosea 2:7) or marriage (Genesis 24:5; 1 Samuel 25:42). Considering Boaz's praise of Ruth's character, it's obvious he means marriage.