The person who is called righteous in the Psalms is not someone who is without sin. However, it is very important for those who belong to the Lord and who live from and by his grace to learn to see and refer to themselves as the righteous. God’s people are only in the second instance sinners. United with the righteous One, Jesus Christ, believers are no longer living under sin.
The righteous are the people of God who serve him by faith and take God’s covenant with his people seriously. The righteous are recognized by their service to the Lord and their fear of the Lord. They are the ones who take God’s covenantal promises seriously in faith and truly live by them. In the Psalms, they are described as the upright, the poor, the weak, the pure, the holy, God’s servant, the needy, the humble, those who love God’s Name, those who seek the Lord, those who keep the Lord’s words and covenant, the man who trusts in the Lord, those who weep for Zion, etc.
The book of Psalms makes an important distinction between the righteous and the unrighteous, indicating the different destinies. Psalm 1 portrays this distinction in a vivid way, and the rest of the Psalter expands upon it. Only through recognizing yourself as a righteous person can the Psalms truly become songs of joy and pain(!) on your lips!
1 Blessed is the man who walks not in the counsel of the wicked, nor stands in the way of sinners, nor sits in the seat of scoffers;