When you boil down something, you get it down to its essence. A summary of a book should boil down the story to the main idea. In cooking, it literally means to reduce liquid by boiling off the water.
As you boil down a sauce, stew, pudding, or other dish, you decrease the water or other liquid in it — it evaporates in the steam rising from your pan. Another way to say this is that you reduce the sauce. Cooks do this to make something thicker and more flavorful. You can also use the phrase to mean become, or be, essentially one basic thing: "Our disagreement boils down to this: I just can't stand scary movies and you love them."