What does Romans 9:15 mean?

Paul has rejected the idea that God was being unjust in choosing Jacob and not Esau to receive His covenant promises before the twin boys were even born (Romans 9:12–14).

Now Paul quotes God's words to Moses from Exodus 33:19. God was providing reassurance that He would be with Moses while leading the children of Israel. In fact, God was preparing to reveal Himself to Moses by passing by and allowing Moses to see a glimpse of his glory. He had agreed to show Moses a physical manifestation of His true nature (Exodus 33:21–23).

In that context, God said that He would show mercy and compassion on whomever He so chose. The right to decide who received benefits from God was a decision left to exactly one being: God Himself. Paul offers this quote to show that God retains the right choose for Himself, based only on Himself, to whom He will give His favor. God is under no obligation, whatsoever, to rely on other criteria or some "higher" standard to make such a choice.

Perhaps that's not a very convincing argument against the idea that God is "unfair" in choosing one over another. However, this already eliminates the suggestion that God is being "unjust." And, as this passage shows, Paul is not yet done making his case.