What does Romans 2:13 mean?

Some of Paul's Jewish readers had made the mistake of thinking that by simply being Jewish, they would be declared righteous by God and spared from His wrath for their sin. After all, they were under the law of Moses. Most Jewish people grew up listening to the books of the Law read aloud from the time they were infants. By definition, they were "hearers" of the law. They knew the words. They understood the big ideas. And they were part of the chosen people of Israel.

Paul argues that just being under the law and hearing it regularly was not enough to save anyone. Hearing the words of Moses's law could not making anyone righteous. In order to be declared righteous in God's eyes, one must obey the law. In fact, Paul will later point out that a person living under the law would have to obey the law perfectly, in every way, in order to be declared righteous by God. Nobody was able to do that until Jesus arrived.

This passage of Romans parallels the message of the book of Hebrews, which clarifies how the old covenant, including the law of Moses, was never meant to save man from sin. It was only meant to teach mankind, to prepare them to accept a Savior (Hebrews 10:1–10).