All three synoptic gospels describe the cup as containing the blood of the covenant, as do Paul's Passover instructions in I Corinthians 11. Matthew adds here that the blood also accomplishes the remission of sins. Notice, though, that the remission of sins does not stand on its own, but it comes through the New Covenant. That covenant contains the forgiveness of sins, but also includes much more (Jeremiah 31:33-34; Hebrews 8:10-12; 10:16-18).
In His Passover prayer in John 17, Jesus includes another aspect of the New Covenant, that of knowing the Father and Him. This covenant allows for those entering the covenant to have a relationship far beyond what the previous covenant offered - to actually know the Father and the Son. Jesus calls this relationship eternal life. It is a life of abundance - foremost spiritual - that continues past the grave in the resurrection.
Rest from Sin and Spiritual Warfare - which God's saints have had to endure since their calling. When Satan is bound (Revelation 20:2-3) humanity will experience relief from continuous deception and temptation, allowing widespread knowledge of Almighty God (Isaiah 11:9): proclaiming The earth shall be full of the knowledge of the Lord as the waters cover the sea). This abundance of knowledge, also described in Hebrews 8:10; 10:16; and Jeremiah 31:31-34, represents the fulfillment of God's sanctification process, in which believers enter a state of holiness and direct communion with Christ.
Now in Ezekiel 11:19; 36:26, and Jeremiah 31:33, we see a promise from God to write this law upon the minds of those He will make the New Covenant with. He is actually going to take away the stony heart and put a heart of flesh within them.
