Here’s an easy-to-understand illustration from Douglas J. Moo‘s Encountering the Book of Romans: A Theological Survey (Grand Rapids: Baker, 2002). It’s entitled “The Many Uses of Quotations” (p. 161):

We have encountered several places in Romans where Paul does not seem to apply the Old Testament in quite the way the original Old Testament context would seem to validate. This creates a theological problem. How can a New Testament writer use the Old Testament to claim that something is true when the Old Testament does not even teach what he claims it does? Such a procedure would be like our trying to prove a doctrine from a text that we have misunderstood. Understandably, we would convince few people. Answers to this problem, which theologians have discussed for years, are not simple. In fact, each of the texts has to be taken on its own, because they present different kinds of problems. But one part of the solution is to recognize that New Testament writers sometimes use the Old Testament not to prove a point but to borrow its language and ethos. An illustration will make the point.

When I was young, and my sons were even younger, we often played basketball out on the driveway together. Then I, and they, grew. I became weaker and slower; they became bigger, stronger, and faster. Foolishly, I kept trying to compete. One day, I was playing one-on-one with my third son, Lukas. He had grown to about six feet six inches and 240 pounds, and was a very strong, highly skilled basketball player. I warned him, “Watch out, Luke, I’m going to take the ball to the basket on you!” He shot back, “Go ahead, Dad, make my day.” He was “quoting” the lines of the character Dirty Harry from the movie starring Clint Eastwood. Eastwood, portraying a cop, uses these words to dare a criminal to draw his gun on him. Luke did not have a gun; he was not threatening to shoot me. He did not intend to quote the author’s “original intention,” nor did I think that he was doing so. The language was a striking way of making a point: if I was foolish enough to try to take the ball to the basket on Luke, I could very well suffer the violence that Dirty Harry’s bad guy suffered in the movie. The quotation worked because we both knew the movie; it therefore communicated the point very well. So Paul and other New Testament writers often use Old Testament language. They know that their readers will understand it, and the application of the language often helps them to perceive a situation in a new light. Thus, in Romans 10:18, for instance, Paul quotes Psalm 19:4 not because he thinks that this text speaks directly about the preaching of the gospel to Israel; rather, he quotes it because the words would awaken echoes in his readers’ minds that would lend force to his assertion.

Related: See G. K. Beale and D. A. Carson, eds., “Introduction,” in Commentary on the New Testament Use of the Old Testament (Grand Rapids: Baker, 2007), pp. xxiv–xxvi. (Cf. my post on this volume.)