One of the biggest changes between the Old and New Covenants is how sin was handled.
In the Old Covenant, God established the priesthood to provide a way for the Israelites to cover or atone for sin—the breaking of the law. The high priest offered a blood sacrifice each year in the Holy of Holies to cover the sins of the people. When the high priest failed, the people had no approach to God.
In contrast, the blood of Jesus did not just cover over our sins; it eradicated our sins.
Jesus shed His blood for man as an everlasting offering in the New Covenant so that we could go boldly to the throne of grace and find mercy and grace to help anytime we need it (Hebrews 4:16). He finished the Abrahamic Covenant by becoming the last sacrifice for sins forever to be offered. His blood did away with the “handwriting of ordinances that were against us” (Colossians 2:14). The New Living Translation says He “canceled the record of the charges against us and took it away by nailing it to the cross.”
To put it another way, the blood of animals (Old Covenant) atoned, or covered, sin (Hebrews 10). The blood of Jesus (New Covenant) remitted—put away—sin once and for all: “But our High Priest offered himself to God as a single sacrifice for sins, good for all time. Then he sat down in the place of honor at God’s right hand” (Hebrews 10:12).
Jesus is the go-between, or the mediator, between God and man (Hebrews 8:6). He is the only way back into the presence of God (Acts 4:12). The moment we make Jesus our Lord, we enter into a blood-covenant relationship with God. All that the Father has, He turned over to Jesus in the New Covenant (John 16:15). We become joint heirs with Jesus in the new-birth experience (Romans 8:17). God’s riches and best become ours!
Source: Kenneth Copeland Ministries