What does Romans 4:2 mean?

Paul has spent much of this letter to the Romans making the point that nobody can be justified—shown to be righteous—before God by following the works of the law. Nobody can escape God's angry judgment for their personal sin, since all have sinned (Romans 3:10).

Now Paul has turned to Israel's primary ancestor, "father" Abraham. He is the ultimate example proving that being made right with God comes through faith and not through works. Hypothetically, Paul says, if Abraham had been justified before God by his works, he would have something to brag about. Of course, nobody can be justified by their works. Even if Abraham were justified in this way, though, meaning that he had never sinned and had only done good works, Abraham would not be able to boast about that to God. God, who is holy and sinless and perfect, would not be impressed with a human being's good works.

Human beings simply cannot be justified before God based on our own efforts.