What does Romans 9:16 mean?

Paul is making the case that God deciding who will receive His favor, or His mercy—and who will not—is not unjust. In the previous verse, Paul quoted God's words to Moses: that He would show mercy and compassion on whomever He chose to, or not, accordingly only to His own will. Another way of putting it might be that God retains the right to give His mercy to whomever He wants. He's not obliged to do anything for anyone, so God choosing some for mercy and not others cannot be unfair in the negative sense that word most often means. In fact, the most "fair" thing to do would be to withhold mercy from all people; mercy is a benevolent form of "unfair" treatment.

Now Paul makes it clear that receiving God's mercy, or not, has nothing to do with human will or work. God is not being unfair, in choosing only some for mercy. No person can ever earn His mercy, so nobody has more of a claim to deserve it than any other. God owes His mercy to absolutely, positively no one. By definition, "mercy" is something given to those who do not deserve it or have not earned it. If it's earned or deserved, it's not an issue of grace or mercy, an idea Paul frequently uses in this letter (Romans 4:2–5; 11:6).

In the following verse, Paul will offer one additional Old Testament example, about a time God chose to particularly withhold mercy for His own purposes.