What does Romans 2:8 mean?

Paul is making clear to his readers that God will indeed judge each one of us according to our works. If somehow we were able to lead lives full of persistent and ongoing good works, God would give to us eternal life (Romans 2:7). However, Paul will show in Romans 3 that none of us are able to lead such lives. In a sense, then, works "would have" been able to save mankind, if we were perfect. But we are not, and cannot be, and so good works can in no way, shape, or form result in forgiveness for our sins.

Now Paul addresses the alternative to those who seek God by obeying His will and His word. God will give "wrath and fury" to those who are self-seeking and don't obey His truth. Instead, these people obey their own unrighteous desires. Having seen this, God will express His anger toward them in judgment.

Paul is building his case that none of us can hope to stand before God on our own merits and receive anything but the judgment we have earned with our sinfulness. We need another way to be saved, and Paul will reveal that it is through faith in Jesus standing before God in our place (Romans 3:22–25).