A "maschil", a psalm of contemplation and teaching, especially in respect of repentance and restoration, following the experience of Ps 51.
v1-2: Who can forgive sins but God alone? The joy of sins forgiven, the penalty cancelled; no wonder David is "blessed", Rom 4.4-8.
Transgression is forgiven, referring to specific wrong-doing.
Sin is covered; there is atonement for the fallen human nature.
Iniquity is not imputed; our falling short is not recorded by God.
No guile; our response must be in integrity and humility; this was true of the Lord Jesus, Is 53.9 quoted in 1 Pet 2.22.
v3-4: The folly of not confessing sins; after David's adultery it was months before he repented; see 2 Sam 11.27; 12.15; his child had already been born before Nathan had come to David. These verses describe his experience. Day and night he had guilt in his heart, perhaps like the nation itself, enduring a summer of drought. 'Often, if we have unresolved guilt in our soul, it will eventualy show in physical stress on the bidy.' (Stephen Kneale, the pastor with a thorn in his side)
v5: The response of repentance, using the same words as in v1-2, sin, iniquity, transgressions; see Prov 28.13.
We are commanded to confess our sins to God, 1 John 1.9; not to offer excuses, for we can have none. Faith in Jesus Christ is not just a matter of superficial improvement, but of radical change, including the renouncing of all sins.
God forgives; we must receive His forgiveness, not because sin is trivial, but because His mercy is great.
v6: As in other psalms, David looks to God to bring blessing to others from his experiences. There is a security in God, which an act of sin cannot destroy.
v7: God knows our frailty, and He preserves us, and gives us songs of deliverance; we enjoy His presence in difficult times, Ps 23.5.
When we think we are surrounded by trouble, we find God protects us from trouble AND surrounds us with songs of deliverance.
v8: God knows our uncertainty, and will guide us; this is not just the matter of a subjective inner voice, for it involves instruction and teaching, Ps 25.9-10.
v9: Horse and mule need, respectively, restraint and motivation; they lack understanding, and need human control and direction, with "bit and bridle."
v10-11: Blessing on the righteous; as we experience God's forgiveness, we can rejoice in Him. Where there is a failure to obey and a failure to confess our sins, we lose our joy in Him.