This piece is from the incredible setting of Psalm 51, the "Miserere", composed by Gregorio Allegri in the 1630s for the Pope's own Holy Week observances.
The Psalm expresses the deep contrition we should feel for sins committed against an all-loving God; the haunting beauty of this piece also captures some of the emotion of the Prodigal Son's appeal, which must have been so beautiful to the ears of the Father Who desired his return. At the end, listen for the slight change in tone to a hopeful sound, echoing the hope we have in God's mercy and forgiveness (symbolized by the Psalmist's description of the rebuilding of Jerusalem).
Translation of the clip: "Have mercy on me, O God, according to thy steadfast love; according to thy abundant mercy blot out my transgressions.
Wash me thoroughly from my iniquity, and cleanse me from my sin!
For I know my transgressions, and my sin is ever before me.
Against thee, thee only, have I sinned, and done that which is evil in thy sight, so that thou art justified in thy sentence and blameless in thy judgment...
The sacrifice acceptable to God is a broken spirit; a broken and contrite heart, O God, thou wilt not despise.
Do good to Zion in thy good pleasure; rebuild the walls of Jerusalem, then wilt thou delight in right sacrifices, in burnt offerings and whole burnt offerings; then bulls will be offered on thy altar."