Leviticus 17:11 explains the theological importance of blood in Israel's sacrificial system: the life of the flesh is in the blood, and God has given it upon the altar to make atonement. Blood represents a life given in place of another, making the sacrificial system a vivid reminder that reconciliation with a holy God involves the cost of life.
Jesus uses this same sacrificial framework at the Last Supper when He speaks of His blood being poured out for many for the forgiveness of sins. Mark 10:45 likewise says that the Son of Man came to give His life as a ransom for many. Leviticus 17:11 is not a direct prediction of the words or circumstances of Jesus' death, but it supplies the biblical theology by which His death is understood. Christ gives His own life rather than the life of an animal, and His self-offering provides the redemptive sacrifice to which the earlier blood offerings pointed.