What does Psalm 51:13 mean?

David wanted to be forgiven and restored to a close walk with the Lord, and he believed the Lord's mercies would reinstate him as God's faithful servant. Once again, he would be able to teach transgressors God's ways—how He wants His people to live—and restore sinners to God.

When a believer sins, he damages his testimony, fellowship with the Lord, and effectiveness. He needs to be restored. In Galatians 6:1 the apostle Paul called upon "spiritual" believers to restore a fallen believer "in a spirit of gentleness" and be careful lest they, too, would be tempted. "Restore" means to bring back into alignment. Just as a dislocated limb is ineffective and needs to be put back in place, even so a fallen believer is ineffective and needs to be put back in his proper place in the body of Christ. They don't need to be re-saved, since true salvation can never be lost.

When Peter denied the Lord, he needed to be restored. Graciously, the Lord restored him and gave him the assignment to feed the Lord's sheep (John 21:15–19). If we fall to temptation, we do not have to stay down, the Lord can lift us up and get us back on track.