For the life of the flesh is in the blood, and I have given it for you on the altar to make atonement for your souls, for it is the blood that makes atonement by the life.” (Leviticus 17:11, ESV)

The context of this verse is that God is forbidding the Israelites from eating the blood of animals.  One reason for this prohibition was that blood was used to make atonement for their lives. The Bible Knowledge Commentary says here:

(God has chosen sacrificial blood as the ransom price for a person’s life, so the life of a substitute is given up in death); therefore to refrain from eating blood is to show respect for its sacredness as a vehicle of atonement.

The Hebrew word that the ESV translates to make atonement is one of the most theologically important words in the Old Testament.  It signified something (animal blood) in place of something else (man’s own blood) for the forgiveness of sins.  The passage is clear here: it is the blood that makes atonement by the life.

The point of all of this becomes strikingly clear in Christ Jesus and the writers of the New Testament, being Hebrew (except for Luke) and very familiar with Hebrew theology understood this well. Paul writes:

In him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace,” (Ephesians 1:7, ESV)

Without the rich symbolism of the blood of animals making atonement in Leviticus, this statement would make no sense at all.  No longer do we need animal blood to make atonement for our sins [which are many].  Our sins were paid once for all through Christ’s atoning death at the cross.  Or as the hymn writer put it:

There is a fountain filled with blood
Drawn from Immanuel’s veins;
And sinners, plunged beneath that flood,
Lose all their guilty stains:
E’er since by faith I saw the stream
Thy flowing wounds supply,
Redeeming love has been my theme,
And shall be till I die:

When this poor lisping, stammering tongue
Lies silent in the grave,
Then in a nobler, sweeter song,
I’ll sing Thy power to save: