I'm a beginner in algebraic geometry. Recently, I learned about constructible sets and Chevalley's theorem. In a Noetherian space, constructible sets are some kind of finite union of open and closed sets, and Chevalley's theorem states that if $f : X \to Y$ is a morphism of finite type between Noetherian schemes, then the image of any constructible set $C \subset X$ is also constructible.
Is there any good application of the theorem? I can't understand why we have to consider constructible sets. It resembles Borel sets in measure theory (but the situation is completely different since topology is far from Hausdorff), so maybe we can think of constructible sets as some sort of topologically simple sets. But such intuition doesn't give any result.