I just finished N.T. Wright's fantastic "Scripture and the Authority of God." In it, he presents a "five-act" way of interpreting the Biblical writings. The five acts are: creation, fall, Israel, Jesus, and the church. In the same way that a play follows various acts, so to does God's history and narrative. The Bible is the telling of that narrative with the Old Testament telling the first three acts, the Gospels telling the fourth, and the rest of the New Testament telling the fifth, which we are currently living in. In this way, Wright tells us that "the fifth act goes on, but its first scene is non-negotiable, and remains the standard by which the various improvisations of subsequent scenes are to be judged."
In relation specifically to what Paul is saying, Wright says that "we who call ourselves Christians must be totally committed to telling the story of Jesus both as the climax of Israel's story and as the foundation of our own." This fact is what Paul is trying to draw the Corinthians' attention to. When we fail to put the Old Testament in context as the first three acts of a five act play, we miss so much of its meaning. By seeing the Old Testament as somehow separate from the New Testament we err, but in two divergent ways.
The Pharisees and other religious leaders of Jesus' time saw the Old Testament is the entire story. They thought that the narrative was only the first three acts. Because of this, they missed out on the blessings of the final two acts and failed to fully understand what the first three acts meant. In contrast, far too many Christians today see the Old Testament as a separate play from the New Testament. The Old Testament in this case becomes pointless. It has some interesting history, but that has no impact upon our lives today. On this view, Jesus was not the start of a new act on the overall narrative, He was the start of a completely new narrative.
Both of these views fail to grasp the entire picture that God is painting and the story that He makes us a part of.
Finally, here is one part of Wright's book that I found especially insightful. I wanted to give the book a standing ovation when I read it. The book is chock of fantastic insights such as this. In fact, I loved it so much, here's a link to buy it on Amazon.
It is vital that we understand scripture, and our relation to it, in terms of some kind of overarching narrative which makes sense of the texts. We cannot reduce scripture to a set of "timeless truths" on the one hand, or to mere fuel for devotion on the other, without being deeply disloyal, at a structural level, to scripture itself.