Sin entered into the world through one man, Adam. Death came through sin. Death passed unto all men, for that all sinned. (Romans 5.12 and Romans 3.23)
The wages of sin is death (Romans 6.23). We all should have died. In his love, the Lord has found the solution to save us. Sin had to be punished, but the Lord wanted to save from death the human being whom he had created.
In the Old Testament, God gave a law to the Jews about the atoning sacrifice for their sins. They had to bring to the temple animals that were sacrificed on the altar, because apart from shedding of blood there is no remission (Hebrews 9.22). According to the law, almost all things are cleansed with blood. (Hebrews 9.22) The human guilt was transferred to the animal. The life of the flesh is in the blood. It is the blood that makes atonement for their souls. (Leviticus 17.11)
The Jews were not allowed to eat the flesh with the blood in it, for the blood is the life (the soul) (Deuteronomy 12.23). Everything that was done under the old covenant was an anticipation of what Jesus is going to do under the new covenant.
Slaughtered animals only postponed the punishment for the human guilt, for it is impossible that the blood of bulls and goats should take away sins (Hebrews 10.4).
Jesus Christ, the Son of God, came as the divine Lamb, a lamb without blemish and without spot (1 Peter 1.18, 19). He gave Himself for us out of love, once for all. His sacrifice is sufficient and perfect. God set Him forth to be a propitiation, through faith, by his blood (Romans 3.25) Jesus died in our place.
In the old covenant, the high priest alone entered into the Holy of holies of the tabernacle, once a year, with the blood of the animals, to make atonement for himself and for the errors of the people: (Hebrews 9.7). Jesus, our High Priest, entered once for all, into the holy place (the Holy of holies) in the heavenly tabernacle with His own blood, having obtained eternal redemption for us. (Hebrews 9.12)
Here is what the Bible teaches about this:
1) In the new covenant, the blood of Jesus makes atonement for our sins, just as in the old covenant the blood of animals made atonement for sin (Leviticus 17.11)
2) The blood of Jesus protects us from death (spiritual death), just as the blood of a lamb slaughtered in Egypt and placed upon the lintel protected the Jews from the Destroyer. (Exodus 12.21-23)
3The blood of Jesus is the blood of the new covenant (New Testament), which is shed for many for the remission of sins. (Matthew 26.28, Mark 14.24 and Luke 22.20)
4Jesus purchased His church with his own blood. (Acts 20.28)
5) By His blood we are justified (Romans 5.9). Jesus paid the price for our sins. We are safe from the wrath of God.
6) By the blood of Christ, we were made nigh from God (Ephesians 2.13)
7) Through the blood of His cross, God made peace, reconciling unto Himself through Jesus all things, whether things upon the earth, or things in the heavens. (Colossians 1.20)
8) We were redeemed to God with the precious blood of Christ (1 Peter 1.18, 19, Revelation 5. 9)
9) By the blood of Jesus we have boldness to enter into the holiest. (Hebrews 10.19)
10) The blood of Jesus Christ cleanses us from all sin (1 John 1.7, Revelation 1.5 and Revelation 7.14)
11) The blood of Christ cleanses our conscience from dead works to serve the living God
(Hebrews 9.14)
12) Jesus sanctified the people (of God →Strong grec 2992) through His own blood (Hebrews 13.12)
13) John heard a great voice in heaven, saying that the saints (brothers) overcame Satan because of the blood of the Lamb and because of the word of their testimony (Revelation 12.11)