What does Romans 3:14 mean?

In this passage, Paul is pointing out that no person—not even one—can claim to be righteous on the basis of our own efforts. Starting with the often-quoted verse 10, Paul cited an Old Testament Scripture which supported his point, beginning with Psalm 14. After making this point through verse 12, Paul moved to uncover the way humans use our bodies to express our sinfulness. He began in the previous verse with the throat, tongue, and lips; these are references to human speech. He quoted from the Old Testament to back up his statement that all people, Jews and Gentiles alike, are under sin and accountable to God's judgment.

Now Paul continues by quoting what the writer of Psalm 10:7 said about the mouths of the wicked. Paul is making the case that all of us are, by nature, wicked. Our mouths are full of curses or cursing. Based on the language and context, this is likely a reference to calling for bad things to happen to each other, as opposed to profanity or other forms of swearing. In addition, our mouths are also full of bitterness. In other words, we use our mouths to express our resentment and hatred toward other people made in God's image, wishing for harm to come to them.