We can use this psalm to seek God's forgiveness and to pray for inner renewal by the Holy Spirit.
The psalmist's plea extends beyond a desire for a physical cure (that cure is a sign that his sin has been forgiven). He begs God to renew his inner being by an act of creation (v. 10), which will allow him to dwell in the presence of God and share in the life that he possesses and bestows. The psalmist speaks of the fidelity to God which the prophets have said will appear in the New Covenant that God will make with his people (cf. Jeremiah 24:7; 31:33; Ezekiel 36:25-27).
This psalm arrangement is used in the Mass liturgy on the Thursday of the 20th Week in Ordinary Time, Year 2.