Psalm 14 and Psalm 53 are both written by David and say almost exactly the same thing except for a few wording differences. Why did David duplicate these Psalms?
Well, both Psalm 14 and Psalm 53 are famous as the Psalms that tell us what God thinks of people who don't believe in him. The fool has said in his heart, "There is no God." Now in Scripture, a fool, it's not making fun of somebody, it's not saying that they're dumb or that they're stupid. It's saying that they have not chosen to follow after God. That's a fool in Proverbs. That's a fool in Psalms. But just two issues here, Psalm 14 and Psalm 53 are nearly identical. First of all, Psalm 14 stands on its own, but it is repeated in Psalm 53 because Psalm 53 is part of a trilogy. Psalm 52, 53, and 54 all go together and they all reflect a particular time in King David's life. And so it's repeated for that reason because in the the second part, Psalm 53, it becomes part two of this little trilogy of David's life.
But on a bigger stage, any time Scripture repeats itself, that's a clear way of God saying, "Pay attention to this." And obviously we're to pay attention to all of Scripture, but how gracious is he? Something as important as the fool has said in his heart, "There is no God," gets repeated for us in the Psalms. So anytime the Scripture repeats itself, we're called to pay attention, doubly so.