What does Romans 2:10 mean?

Paul restates something similar to what he wrote in verse 7. God is completely fair and impartial with humanity. He will judge each person according to that person's own works, not the works of family, or their community, or their nation. If a person were able to lead a life full of ongoing unselfish good works, God would reward that person with glory and honor and peace. Verse 7 went further: God would give them eternal life. Of course, as Paul will show later, that kind of perfection is not possible for sinful mankind (Romans 3:23).

Paul writes again that this reward would be given first to the Jewish people and then to the Greeks—here meaning the same thing as Gentiles, or non-Jews. In other words, it's the same for all, no matter of race or nationality. Paul will show in the following chapter that none of us are able lead such a life. We simply cannot, do not, "do good." Instead, every last one of us, by nature, turns away from God and becomes worthless (Romans 3:12).

So what hope do we have? That's why Paul is writing this letter. He will show that our only hope of receiving eternal life, along with glory and honor and peace, is through faith in Christ. We have no hope through our own ability to do good.