The Decalogue, God’s law encapsulated in the Ten Commandments, has three uses: it restrains sin, accuses sinners, and instructs Christians.
Article VI of the Formula of Concord explains the third use of the Decalogue like this:
“. . . the Holy Ghost employs the Law so as to teach the regenerate from it, and to point out and show them in the Ten Commandments what is the [good and] acceptable will of God, Rom. 12:2, in what good works God hath before ordained that they should walk, Eph. 2:10. He exhorts them thereto, and when they are idle, negligent, and rebellious in this matter because of the flesh, He reproves them on that account through the Law, so that He carries on both offices together: He slays and makes alive; He leads into hell and brings up again.”
Thus, the Decalogue is to be preached not only to unbelievers but also to believers because they also have the sinful nature that must be daily crucified so that they can daily rise to new life, a new creation (Romans 6, etc.). Apart from that struggle against the flesh, the new man needs no Decalogue:
“But when man is born anew by the Spirit of God, and liberated from the Law, that is, freed from this driver, and is led by the Spirit of Christ, he lives according to the immutable will of God comprised in the Law, and so far as he is born anew, does everything from a free, cheerful spirit; and these are called not properly works of the Law, but works and fruits of the Spirit, or as St. Paul names it, the law of the mind and the Law of Christ. For such men are no more under the Law, but under grace, as St. Paul says, Rom. 8:2.”
The Christian needs to hear the preaching of the Decalogue only because of the continued presence of the old man, as argued in the beginning of the Formula of Concord’s article on the third use of the law. The law not only restrains and accuses the saint-sinner but also instructs him since the law is not yet completely in his heart. The Holy Spirit writes it there not by the preaching of the law and pastoral pleas to obey it but rather by the preaching of the gospel.
Indeed, the preaching of the gospel, not the preaching of the law, directly renews the Christian, raising him to walk in newness of life and writing the law on his heart. While the preaching of the law does not directly renew the Christian, it does so indirectly by providing instruction that leads to repentance and faith in the gospel.
There is another way in which the preaching of the law indirectly renews the Christian. In obedience to the Sabbath commandment, the Christian hears the gospel and receives the sacraments. By those means, the Holy Spirit sustains and strengthens faith in the gospel and therein renews the Christian for good works.
Oswald Bayer observed that the Formula of Concord echoed the theology of Luther on the third use of the law (Chapter 5 of Living by Faith):
“Luther himself continually stressed the fact that the law should not be preached to Christians insofar as they are justified by the gospel. But it should be preached to them insofar as they are sinners and still belong to the old world. This truth finds the same emphasis in Article VI of the Formula of Concord, which emphatically seeks to clarify ‘what the gospel does, effects, and creates for the new obedience of the believers and what the law does in relationship to the good works of believers.'”
In short, because Christians in this life still have the sinful nature, they need the law to inform them about how what is right in their eyes differs from what is right in God’s eyes, to condemn them, and to restrain them.