“I will bless her, and indeed I will give you a son by her.  Then I will bless her, and she shall be a mother of nations; kings of peoples will come from her.”  Gen. 17:16

God has already told Abraham that kings will come from him (v. 17:6) however the writer of Genesis goes out of their way to make us understand that Sarah was not merely the vessel that God’s promise to Abraham would be fulfilled through; she herself has a share in the blessing1.  The meaning of Sarah’s name becomes more significant now, as this verse explains that kings of peoples will come from her.  This is what Abarim-publications.com says about the origin and meaning of Sarah’s name:

“From sarar (sarar 2295) rule, reign, be princely, govern. The feminine derivation Sarah (sara 2295b; hence Sarah) is used for royal ladies of the court. Before the conception of Isaac Sarah was called Sarai, probably also a derivation of the same word, meaning my princess. Possibly, the name-change indicates a step from local to global, or specific to general”

So with the birth of Isaac will come many peoples, including kings, and so Sarah is a progenitor to royalty, even if she is not technically royalty at this time.  Thus the broadening of the scope of her name will become fulfilled through her descendants.

We can contrast this with the blessings for Ishmael – that he would become the father of twelve princes (Gen. 17:20).  This may be inferring a subservience to the sons of Isaac, as even princes are subservient to kings.

Fox, Everett. The Five Books of Moses: Genesis, Exodus, Leviticus, Numbers and Deuteronomy.  New York, Shocken Books, 1997