What does Romans 3:13 mean?

Paul is quoting from the Old Testament Scriptures, the sacred text that his Jewish readers would recognize and respect. His purpose is to show that his statements about every person being "under sin" are not a new idea. The last few verses drew on Psalm 14, which indicated that God sees a universal trend in humanity towards sin and disobedience. Though we may be able to do good things, sometimes, we all choose not to follow God's goodness all the time. This means nobody—not one person—can be considered "righteous" according to their own efforts.

This and the following verses list several ways people use our human body parts to express our sinful nature. Paul begins with the voice, quoting from Psalm 5:9 where David declares that the throats of his enemies are open graves. This carries two ideas. First, in Jewish thinking, graves are tainted by death, and are therefore corrupt. Anything taken from a grave would be ceremonially unclean. The phrase could also mean that the effect of their words is death and decay. Also from Psalm 5:9, Paul points to the tongue as a source of deception. The deception David referred to was flattery—a dishonest use of words.

Paul moves from throat to tongue to lips and a quote from Psalm 140:3. There, David referred to evil men with the venom of asps—deadly snakes—under their lips. In other words, words from the mouths of his enemies could quickly poison and kill.

Paul's use of David's words here is meant to expand on David's original description. David referred to his enemies' mouths—Paul is pointing to the sins of every single person who has ever lived. We all have used our words, our mouths, for sinful purposes. That is who we are apart from God's help and power.