"Thou desirest not sacrifice; else I would give it: Thou delightest not in burnt offerings. The sacrifices of God are a broken spirit: a broken and contrite heart, O God, Thou will not despise," cried out the Psalmist.
Burdened with a sense of guilt he could no longer endure, he knew going through the formality of offering sacrifices and burnt offerings unto God would not release him from his guilt. His problem went deeper than the outward act that was sin, his heart was sinful. Humbly and penitently he prayed for forgiveness, and received it.
Today, 2000 years this side of Calvary, God still desires and requires a humble spirit and penitent heart of sinners as they come to Christ for forgiveness. He also desires (and requires) obedience, but it must be form the heart, not merely an outward act. God desires that we "present out bodies (whole selves) a living sacrifice, holy, acceptable unto Him." See Romans 12:1. A pure heart full of love and devotion and surrendered to Christ, not religious rites, is what God desires of us.