VINDICATE ME, O GOD...
We are all fallen creatures. Twice in this psalm there's the idea of innocence--washing your hands in innocence, and thus returning to the innocence of Eden.
Innocence involves a purification of our relationships with those with whom we worship in the beauty of the house of God (v. 8). It also involves our relationship with God Himself. This relationship, when restored to its original, innocent position of total dependence on God for everything from our next breath to our mortgage payment, involves not only a real change on our part ("my integrity," v. 11), but an acknowledgement that, even when we do our part, we still require His help ("redeem me, O LORD," the rest of v. 11).
Or, as Fr. Patrick says, "It is from the altar of repentance that we are rendered innocent, purged by a coal so ardent that not even the firery seraph dares to take it except with tongs."
Thought of this today, btw, during Liturgy...the Holy Eucharist is likened to Isaiah's coal, yes, but an even more direct comparison is the blood over the doors of the Israelites when they left Egypt. We, when we place the Blood of the Lamb on our mouths--one of the "doors" of the body, our senses--we prepare ourselves for death, knowing that death will pass over us when it sees the Blood of the Lamb.