A covenant is a mutual consent or agreement of two or more persons.
Under the old covenant, our sin could be covered by the sacrifices of animals, but never removed. The sense of guilt connected to sin was always present.
But the good news is that God has made a new covenant with man. It is a better covenant — far superior to the old. The old covenant was initiated with the blood of animals, but the new was initiated with the sinless blood of Jesus Christ.
Jesus took the punishment that we deserved, and promised that if we would believe in Him and all that He did for us, He would forever stand in our place, and our responsibility to keep the law would be met in Him. The old covenant focused on what man could do, but the new covenant focuses on what God has done for us in Jesus Christ (see Romans 5).
You CAN read the Bible through in a year. Start today!
Mon: 1 Corinthians 16, Matthew 3:7-10, Psalm 75, Proverb 31:31
Tues: 1 Thess 4:1-5, 2 Cor 5:14-21, Psalm 77:11-20, Prov 9:10-12
Wed: Romans 13:12-14:19, John 1:1-14
Thurs: 1 Corinthians 1-4, Matt 3:11-17, Psalm 90:1-6, Proverb 1:1-4
Fri: 1 Corinthians 5-8, Matt 4:1-11, Psalm 90:7-12, Prov 1:5-7
Sat:1 Corinthians 9-11, Matt 4:12-17, Psalm 90:13-17, Pro 1:8-9
Sun: 1 Corinthians 13, Ephesians 3:14-21, John 15:1-17

This is the covenant that I will make with them after those days, declares the Lord: I will put my laws on their hearts, and write them on their minds.
Hebrews 10:16