"Jeremiah heard God say that he would make a new covenant with the people, not like the covenant that he had once made with their fathers. This would be a covenant, not established by an externally imposed law, but written on their hearts and in their inward parts. It would be a covenant in which all men really and truly knew God. ‘I will forgive their iniquity,’ God said, ‘and I will remember their sin no more’ (Jer. 31.31-35). Two things stand out about this new covenant; it is a covenant based not on law but on the inward devotion of the heart, and there is no mention of sacrifice at all.
"Two things are to be noted in the words of Jesus, as Paul relates them—‘This cup is the new covenant in my blood’ (I Cor. 11.25). Jeremiah also speaks of the new covenant (Jer. 31.31; LXX 38.31). Both in Paul and in the Greek of Jeremiah the word for ‘new’ is kainos. Greek has two words for ‘new.’ There is neos, which is new only in point of time; a thing which is neos may simply be the most recent example or specimen of something which has for long existed and which has for long been produced. But kainos means not only new in point of time, but also new in point of kind or quality. With a thing which is kainos a new quality has entered into life and the world. Since that is so, a new (kainos) covenant is not simply an old covenant which has been renewed or restated; it is a covenant of a new and different kind. Second, Jesus says of this new covenant that it is in his blood. The Greek word for in is en; en can and does translate the Hebrew word be, which means at the price of. It may, therefore, well be that Jesus said that this new and different kind of covenant is made possible only at the cost and at the price of his blood. When we put this together, we see that Jesus said that a new relationship between man and God has become possible through his blood, that is, through his life and death…
"What, then, was Jesus doing in his life and in his death? The answer must be that in his life and in his death Jesus was demonstrating to men the eternal, unchangeable, unconquerable love of God. He was demonstrating to men that God is the Father who loves undefeatably and whose one desire is that the lost son should come home. When Jesus entered the world, when he healed the sick, comforted the sad, fed the hungry, forgave his enemies, he was saying to men: ‘God loves you like that.’ When he died upon the cross, he was saying: ‘Nothing that men can ever do to God will stop God loving them. There is no limit to the love of God. There is no end beyond which that love will not go. God loves you like that.’ That is why nothing less than death on the Cross would do. If Jesus had refused or escaped the Cross, if he had not died, it would have meant that there was some point in suffering and sorrow at which the love of God stopped; there was some point beyond which forgiveness was impossible. But the Cross is God saying in Jesus: ‘There is no limit to which my love will not go and no sin which my love cannot forgive.’"
William Barclay, Crucified and Crowned