"The New is in the Old concealed; the Old is in the New revealed." (attributed to Augustine)
In many church services, there are readings from both the Old and the New Covenant. I prefer the term Covenant, rather than the more familiar Testament, because it reminds us that the Bible is a covenant document. That is, it is a book of promises that God guarantees by the blood of his own Son, Jesus Christ. The Old Covenant consists of thirty-nine inspired books that were written before the coming of Christ; the New Covenant consists of twenty-seven inspired books (including the four Gospels) that were written after the coming of Christ.
But why read from both the Old and the New Covenants?
One answer is simply that this is a healthy exercise to increase our familiarity with both the Old and the New Covenants/Testaments. Many people know very little about the Old Testament, and even question its relevance for our day. Regular readings from the Old Testament (as well as the New), perhaps accompanied by the minister's brief comments preceding the readings, help the congregation to better appreciate portions of the Scriptures that would otherwise be foreign to them.
The other reason is that readings from the Old and the New Covenants together serve to remind us that the New Covenant is a fulfillment of the Old, and the Old is a prophecy of the New. Both the Old and the New Covenants have their focus on Jesus Christ and his everlasting kingdom. In hearing them together, we increasingly understand how the New Covenant uses portions of the Old, and we increasingly understand how the Old Covenant includes the themes that are unwrapped in the New.
The total effect is not only to help us to understand the Bible better, but also, above all, to prepare us for the ministry of the Word, which also focuses on Christ and his redeeming work in all of the Scriptures.