Romans says all people are under sin: both Jews and Greeks stand in need of God's mercy. Paul brings together Scripture's witness to show that no one can claim righteousness before God on the basis of their own record.
Romans 3:9-20 gathers the argument from Romans 1-2. Paul has shown Gentile idolatry, Jewish accountability, and the failure of human boasting. The law speaks so every mouth is stopped before God.
This prepares for the good news of Romans 3:21-26. The gospel is not for one type of sinner; it is God's answer to the shared human problem.
The phrase does not mean every person is as evil as possible. It means sin has placed all people under guilt and need before God.
Original wording grounded in Romans 3:9-20.