Fat carries flavor. Pure fat, like vegetable oil or shortening, is actually kind of unpleasant to eat. But many of the aromatic compounds that make food taste good or interesting can be easily stored in fat. This is why, for example, garlic butter will do a better job flavoring a dish than just tossing some garlic into the pot. (Even when you do cook with fresh garlic, the standard procedure is to first sauté it in oil. Why? So the oil picks up the garlic flavor). On top of this, fat is very good at coating our mouths, giving a more intense and longer-lasting experience of those flavors.

Especially when it comes to animal products, it might even be more accurate to say that "fat is flavor." The aromatics that make beef taste distinct from pork, for example, are mostly contained in the fats of those animals.