The New Covenant in His Blood

Luke 22:20 "This cup is the new covenant in My blood, which is shed for you."

Matthew 26:28, "For this is my blood of the new covenant, which is shed for many for the remission of sins."

The blood of Jesus was shed for our sins.
It is the sign of a new covenant that has been instituted, a better covenant than the old covenant under Moses.
"But now He [Jesus] has obtained a more excellent ministry, inasmuch as He is also Mediator of a better covenant, which was established on better promises"
Hebrews 8:6.

The essence of covenant is exchange: Jesus took our sin that we might have His righteousness.
"For He [God] made Him [Jesus] who knew no sin to be sin for us, that we might become the righteousness of God in Him"
2 Corinthians 5:21.

Jesus took our curse so that we might have His blessing.
"Christ has redeemed us from the curse of the law, having become a curse for us (for it is written, Cursed is everyone who hangs on a tree). that the blessing of Abraham might come upon the Gentiles in Christ Jesus"  Galatians 3:13,14.

Jesus took our sicknesses that we might have His wholeness.
"Surely He has borne our griefs [literally-sicknesses] and carried our sorrows [literally-pains] He was wounded for our transgressions, He was bruised for our iniquities. The chastisement for our peace was upon Him, and by His stripes we are healed"  Isaiah 53:4,5.