How much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, purify our conscience from dead works to serve the living God. Hebrews 9:14 (ESV)
The priests of the Old Testament offered countless sacrifices for the people and also for themselves. If the blood of those sacrifices had the power to offer purification, how much more will the blood of Christ! Christ is the ultimate sacrifice because His blood is without blemish. He is perfect and the sacrifice of His own life satisfied the penalty of sin completely. His blood has the divine ability to purify our conscience. It washes us deep within and empowers us to serve the living God.
Indeed, under the law almost everything is purified with blood, and without the shedding of blood there is no forgiveness of sins. Hebrews 9:22 (ESV)
There is a legal aspect of the blood of Christ in relation to us. You see, the law requires the shedding of blood in exchange for forgiveness. What Jesus did on the cross is forever sure and we can count on His righteousness. Because of His pure and undefiled blood, we can truly be made clean- even the deepest parts of our conscience.