What does Romans 4:15 mean?

Paul has said flat out in the previous verse that God's promises to Abraham and his descendants, Israel, are worthless if they depend on Israel following the law of Moses. For one thing, the promises were made long before the law existed (Romans 4:13–14). For another thing, nobody is able to keep the law (Romans 3:23). So the promises would be empty, based on a condition that cannot be met. Many of Abraham's descendants never had the law, and even those who did would not be able to keep it!

Paul's primary point comes across more clearly as this letter continues. The law cannot deliver the promises of God, since nobody can keep the law. Instead, Paul now writes, the law brings God's wrath in judgment for human sin, for lawbreaking. Without the law, on the other hand, Paul writes that there is no transgression. Nobody can break a law that doesn't exist, or which doesn't apply to him.

This is not meant to be understood to mean those not under the law have never sinned. Everyone has sinned (Romans 3:23), and has done so without any valid excuse (Romans 1:18–20). Paul simply means that those who are not under the law have not broken the law, specifically.