Jesus Christ spoke of His blood as "My blood of the new covenant, which is shed for many for the remission of sins" (Matthew 26:28).
What is a covenant? A covenant is an agreement or pact between two or more parties. A covenant between God and man centers around God's gracious undertaking for the benefit and blessing of man. For example, God in His covenant with Abraham promised to make Abraham the father of a great nation from which would come one who would bless all nations (Genesis 12:1-3; 22:15-18). God has kept His promise, making Abraham the father of the nation Israel (Deuteronomy 26:5) from which came Messiah, the Savior of the nations (Galatians 3:8,14,16).
What is the "new covenant"? The New Covenant presupposes the Old Covenant, that which God made with Israel at Mount Sinai shortly after bringing them out of Egyptian bondage. The Old Covenant was a conditional covenant, a quid pro quo, God's blessing being conditioned upon Israel's obedience (Exodus 20:5f): "Now therefore, if you will indeed obey My voice and keep My covenant, then you shall be a special treasure to Me above all people; for all the earth is Mine. And you shall be to me a kingdom of priests and a holy nation." The covenant which God required Israel to obey was the Ten Commandments (Exodus 20; 34:28).
Because of Israel's failure to keep the Old Covenant, God prophesied the New Covenant in Jeremiah 31:31-34: "Behold, the days are coming, says the LORD, when I will make a new covenant with the house of Israel and with the house of Judah – not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt, My covenant which they broke, though I was a husband to them, says the LORD. But this is the covenant that I will make with the house of Israel after those days, says the LORD: I will put My law in their minds, and write it on their hearts; and I will be their God, and they shall be My people.... For I will forgive their iniquity, and their sin I will remember no more." The New Covenant instituted by Jesus Christ has replaced the Old Covenant (Hebrews 8).
What is the "blood of the new covenant"? God's covenants with man have been established and confirmed with the shedding of the blood of a sacrifice. Accordingly, Moses confirmed the Old Covenant with the "blood of the covenant" shed by bulls (Exodus 24:8). Jesus Christ has confirmed the New Covenant with His own blood, which He called "My blood of the new covenant."
Why was the blood of the new covenant shed? "My blood of the new covenant ... is shed ... for the remission of sins" (cp. Jeremiah 31:34). "[W]ithout shedding of blood there is no remission" (Hebrews 9:22). "[For] it is the blood that makes atonement for the soul" (Leviticus 17:11).
For whom was the blood of the new covenant shed? "My
blood of the new covenant ... is shed for many." Observe:
1) Many is fewer than all. Jesus Christ died to effect a limited atonement. It applies only to those with whom God has made this New Covenant: "the house of Israel," those of whom God says "I will be their God, and they shall be My people" (Jeremiah 31:33). But New Covenant Israel is not comprised of merely physical descendants of Abraham. Rather, it is "the Israel of God" (Galatians 6:14), the spiritual descendants of Abraham: those Jews and Gentiles who acknowledge themselves as God's children through justifying faith in Jesus Christ (Galatians 3:7-14). They alone will have their sins remitted by the blood of Jesus Christ.
2) But many is more than a few. In glory they shall comprise "a great multitude which no one could number, of all nations, tribes, peoples, and tongues" (Revelation 7:9).
Have you through faith in Jesus Christ ascertained that you will be among them?