Paul knew that many of his Jewish readers assumed that the list of sins and the punishment that followed were not applicable to them. In this statement, he declares that God judges sin. This is true even for sins committed by faithful Jewish followers of the law. They should not assume that they are exempt from God's judgment. In this letter and throughout his entire ministry, Paul lays the foundation for the central theme of his ministry: everyone, including Jews, must be saved by faith in Christ.
As Paul warns, judgmental people cannot justify their own 'righteousness,' for, in passing judgment on others, they also condemn themselves. The self-righteous and hypocritical are judged because they fall far short of God's standards. In the end, all people have sinned and have fallen short of God's standard. Sin is a natural consequence of being a sinner. 
As stated in Scripture, all men are sinners, and there is no measure of moral good deeds or self-righteous behavior that can enable them to attain God's sinless standard. Faith in Christ is the only path to peace with God and right standing with Him.

Dear Heavenly Father, it is through Christ's death that we are redeemed from our sins. Thank You for the truth of the gospel of grace, and thank You for the organized way in which Paul makes it clear that all have sinned and all have fallen short of God's glory. In the end, those who deny Your existence will be judged, as well as the self-righteous who dress themselves up in their own righteousness. The only thing that can save me is what Christ has done for me, not what I have done. 
In Jesus's name I pray. Amen.