What does Genesis 17:16 mean?

In the previous verse, God told Abraham that He was changing Sarai's name to Sarah. Earlier, God had renamed Abram as Abraham, indicating that Abraham would become the father of nations. Now God reveals that Sarah's name change is related to her own destiny as the "mother of nations." From her, as well, will come future kings.

This is the first time the text reveals that Sarah is the one through whom God will keep His covenant promise to make Abraham into a great nation. In chapter 16, Sarah and Abraham seem to have decided that the opportunity for her to birth children to him had passed. Instead, she would have a child with him through her slave Hagar. That boy, Ishmael, is now 13 years old.

God reveals that Sarah will, in fact, give birth to a son of her own with Abraham, a notion Abraham and Sarah had completely abandoned. This assumption was so strong in Abraham's mind that he will literally fall down laughing at the suggestion that Sarah will be known as the mother of nations, as seen in the next verse.