David says that sacrifice is a prayer. It also works the other way around: Prayer is a sacrifice. Why? Because it is a gift of devotion, praise, and thanksgiving that aids in changing a person's nature from his self-centeredness.
Why is prayer a sacrifice? First, it consumes time. We dislike giving time up unless our heart is consumed by what we want to do, and human nature does not want to do spiritual things. Second, prayer requires giving—the giving of one's mind over to thinking about the qualities of God. How else can we thank Him? We give ourselves to the activity of praise—praise for things that He has done. We do that because we have thought about them and because we acknowledge His presence, His activity, in our or somebody else's life.
Prayer is most effective when we act as a mediator, interceding on behalf of others, meaning that we have given our time to thinking about them and their needs. We give our time to go to God and ask for His intervention so to help them change. God acts on our behalf because we sacrificed and begins to change us away from our egocentricity, our self-centeredness. God is training our minds to think about others rather than the self.
In Psalm 40:6-8, the psalmist says that God did not want burnt offerings. Those who were converted under the Old Covenant understood this fact. Paul quotes this passage in the book of Hebrews. In fact, he quotes Jesus Christ as saying it before He ever came to the earth: "Sacrifice and offering You did not want, You did not desire; otherwise, I would have given it to You. But a body you have prepared for me" (Hebrews 10:5).
One can easily make a ritual out of going to services, tithing, getting rid of the leaven, fasting on the Day of Atonement, or even going to the Feast of Tabernacles if our reasons for doing so are perfunctory, we do not understand, or we disagree with the object lesson that God intends we learn from doing them.
When that lawyer asked Jesus in Matthew 22, which is the great commandment of the law, Jesus said, "You shall love the LORD your God with all your heart, with all your soul, and with all your mind; and the second is like it." He quoted Deuteronomy 6:5 and Leviticus 19:18.
What Jesus described is the meaning of a whole burnt offering. The burnt offering of Leviticus 1:1-13 is the offering of an animal, but it pictures the offering of a life lived completely consumed in obedience to living God's way. Nothing will prepare us for the Kingdom of God to be both kings and priests like following, with all of our being, Leviticus 1:1-13 and what that burnt offering means. Jesus did. He lived as a whole burnt offering to God.