24:6
1. The blood of the sacrifice which the people offered was (part of it) sprinkled upon the altar, which signified the people's dedicating themselves to God, and his honour. In the blood of the sacrifices, all the Israelites were presented unto God as living sacrifices, Rom 12:1.
2. The blood of the sacrifice which God had owned and accepted was (the remainder of it) sprinkled, either upon the people themselves, or upon the pillars that represented them, which signified God's conferring his favour upon them, and all the fruits of that favour, and his giving them all the gifts they could desire from a God reconciled to them, and in covenant with them. This part of the ceremony was thus explained, Behold the blood of the covenant; see here how God sealed to you to be a God, and you seal to be to him a people; his promises to you, and yours to him, are yea and amen. Thus our Lord Jesus, the Mediator of the new covenant (of whom Moses was a type) having offered up himself a sacrifice upon the cross, that his blood might be indeed the blood of the covenant, sprinkled it upon the altar in his intercession (Heb 9:12,) and sprinkles it upon his church by his word and ordinances, and the influences and operations of the Spirit of promise by whom we are sealed.
24:1-8 A solemn covenant was made between God and Israel. Very solemn it was, typifying the covenant of grace between God and believers, through Christ. As soon as God separated to himself a peculiar people, he governed them by a written word, as he has done ever since. God's covenants and commands are so just in themselves, and so much for our good, that the more we think of them, and the more plainly and fully they are set before us, the more reason we may see to comply with them. The blood of the sacrifice was sprinkled on the altar, on the book, and on the people. Neither their persons, their moral obedience, nor religious services, would meet with acceptance from a holy God, except through the shedding and sprinkling' of blood. Also the blessings granted unto them were all of mercy; and the Lord would deal with them in kindness. Thus the sinner, by faith in the blood of Christ, renders willing and acceptable obedience.