on that day when, according to my gospel, God judges the secrets of men by Christ Jesus. (ESV)
In general, most people think they are pretty good. In fact, one of the most dangerous beliefs that plagues our culture is that man is by nature good. The reality is, man is not good. This is one of the dominant themes of Paul's letter to the Romans. Paul will remind us again and again that the heart of man is wicked and in rebellion to God's Law.
In the previous verses Paul has described the law of our conscience. Whether you were a Jew and had the Law that God gave to the nation of Israel, or whether you were a Gentile, apart from God's Law you still had some kind of innate code and sense of right and wrong. At times it would condemn you and at times it would excuse you.
Paul says that there is a day coming when we will all be exposed for the sinners that we are. He mentions "that day," when God will judge the secrets of men. When Paul mentions "that day," he is referring to the Day of Judgment. All of us will stand before the judgment of God. On that day there will be no secrets. Everything will be exposed.
It is a terrifying thought to have God looking at everything that you have done. You can fool most people into thinking that you are a good person. But deep down inside you know better. You know that even the law that you do have, you have not always kept. There is a way to escape this terrible judgment. Those who have confessed their sin and placed their faith in Jesus Christ will be forgiven and the punishment they deserve will be given to Christ, who took that punishment on the cross.
Freely confess your sins, public and secret, to God. Ask him to forgive you. Jesus Christ died to pay for the punishment of your sins. What a wonderful Savior!