Ruth 1:9, commentary and pictures

About ten years after Elimelech of Bethlehem took his wife Naomi and his two sons Mahlon and Chilion to live in Moab because of famine in Israel, where the sons married Moabite women Orpah and Ruth, and after Elimelech and both sons died there, the event took place in and near the close of the time of the judges, with Ruth as the grandmother of David, as a side light to the sterner history of that time.
After Naomi heard conditions in Bethlehem were prosperous she determined to return to her former home there, and both daughters-in-law started with her proposing to go with her.
On the way the verse is part of her effort using every argument to dissuade them and urge them to remain with their own people in Moab rather than go on, because she had no more sons to give them and was too old to marry again, speaking as one grieving much for their sakes because the hand of the Lord had gone out against her.

In the verse Naomi wishes that the Lord would grant each widowed daughter-in-law rest.
That rest means a secure, settled, peaceful home and well-being through remarriage in the house of a husband among their own people in Moab, which in her view was every way to their earthly advantage.
The verse then describes the farewell embrace in which she kissed them and they lifted up their voice and wept together as they parted, an ordeal that proves their fidelity.

Orpah at first withstood with tears but eventually accepted this course and turned back to her mother and to her people and to the gods of Moab, so her connection with the people of God ceases forever and her name is mentioned no more.
Ruth refused to return and remained with Naomi and went with her to Bethlehem.
Ruth's choice to go gives Naomi hope because she still has kinsmen in Bethlehem who may preserve the family inheritance and name.
Ruth's steadfast spirit that will not turn back even when invited brings honor with the chief family in Israel, a place among the ancestors of Jesus Christ, preservation of her history in the Bible, and acceptance in the sight of the Lord.