This passage from Exodus is generally considered to be the primary and essential passage describing the formal ratification of the children of Abraham's covenant with the Lord, and it is critical to our understanding of the words of consecration in the Eucharist. 

Here Moses takes half of the blood of the young bulls and splashes it on the altar with the 12 pillars (representing the 12 tribes) and then reads aloud the “book of the covenant” and asks the people to commit themselves to it as their side of the covenant.  When they have done so, Moses splashes what remains of the blood on them, binding them to the Lord (symbolized by the altar) by that blood.

It is important to understand that for the Jews blood was the seat of life and, to a certain extent, identity: under no circumstances whatsoever might anyone drink it or eat meat with the blood still in it.  All blood was sacred, and it had to be returned to the Lord by pouring it into the ground.

All of that comes into play in the words of consecration over the wine, where the celebrant says “Take this, all of you, and drink from it, for this is the chalice of My Blood, the Blood of the new and eternal covenant, which will be poured out for you and for many for the forgiveness of sins.  Do this in memory of Me.” 

These words are an amalgam of the critical words and ideas of four passages in the New Testament: Jesus says “Drink from it, all of you, for this is My Blood of the covenant, which is poured out for many for the forgiveness of sins” (Matthew 26:27-28), “This is My Blood of the covenant, which is poured out for many” (Mark 14:24), “This cup that is poured out for you is the new covenant in My Blood” (Luke 22:19), and “This cup is the new covenant in My Blood.  Do this, as often as you drink it, in remembrance of Me” (I Corinthians 11:25).

This renewed and final covenant is not in the blood of animals but in the blood of God Himself; the God-man Jesus, in His life climaxing in His death, binds humanity to God in a way that breaks down all barriers between us and God: He is now our God and we are His people --- if we do our best to follow that Law of Love that Jesus completed the written Law with.  How close will that bond be?  Consider the last 2-3 chapters of the Book of Revelation...