Read Hebrews 9:11-14
11 But Christ has already come as the High Priest of the good things that are already here. The tent in which he serves is greater and more perfect; it is not a tent made by human hands, that is, it is not a part of this created world. 12When Christ went through the tent and entered once and for all into the Most Holy Place, he did not take the blood of goats and bulls to offer as a sacrifice; rather, he took his own blood and obtained eternal salvation for us. 13The blood of goats and bulls and the ashes of a burnt calf are sprinkled on the people who are ritually unclean, and this purifies them by taking away their ritual impurity. 14Since this is true, how much more is accomplished by the blood of Christ! Through the eternal Spirit he offered himself as a perfect sacrifice to God. His blood will purify our consciences from useless rituals, so that we may serve the living God.
According to Hebrews the sacrificial acts that took place in the temple were rituals that simply made people feel better. But Christ's sacrifice had power - power that purifies the 'conscience'. The meaning of 'conscience' here doesn't just speak to feeling better about past deeds; but also speaks to a purification of our 'consciousness' - so that from the heart we live lives that reflect the heart of God.
Breathe on me breath of God, Fill me with life anew, That I may love what thou dost love, And do what thou wouldst do.