Clarified butter is (unsalted) butter that’s been melted, then simmered slightly to evaporate off some of the water in it, and cause the non-fat components of the butter (proteins and other miscellaneous stuff) to separate out of it. You know that white foam that collects on a pool of melted butter? Bingo, that’s them.
What’s the point of clarifying butter? Many peoples of the world clarify butter so that a) it keeps longer and b) they can use it as a frying medium. For without all those extraneous molecules, clarified butter has a much higher smoke point than regular butter, i.e. it can be heated to a higher temperature without burning.
However the process of clarifying butter also does another thing: it changes the butter’s flavor. The degree of the change depends on how long and at how high a temperature it’s heated. A little heat and it stays pretty much like standard butter. A little more and the milk solids start to get brown and toasty, creating a slightly darker version of clarified butter. A little more and the milk solids actually burn, creating what’s known in cooking circles as “brown butter”.
For baking purposes, the mid-point is preferred, as butter that’s “cooked” to that degree adds very welcome savory overtones to whatever it’s added to. I like it in brioche and some cake batters, since it provides a nice depth of flavor for relatively little effort. Allow me to demonstrate…