Butter is made up of butterfat, milk solids and water. Unsalted butter is melted over low heat and allowed to separate into butterfat and milk solids. You can further brown or essentially fry the separated milk solids, and it is called Brown Butter or Browned Butter (Beurre Noisette). It has a nutty flavor, and is used batters for madeleines and financiers, or even pasta or vegetable dishes. Clarified butter in some countries, is the translucent golden-yellow butterfat left over after the milk solids and water residue are removed during cooking. 

This how to baking technique is used with the:
Madeleines Recipe

Browned Butter Spoon Cookies Recipe Redux

Browned-Butter Cinnamon Cookie Sticks Recipe

HOW TO TIPS:
INGREDIENTS
Clarified or browned butter will be only 75% the volume or weight of whole butter:
1 cup (2 sticks or 1/2 pound) butter = 3/4 cup clarified or browned butter. 
4 tablespoons butter = 3 tablespoons clarified or browned butter

INSTRUCTIONS
1. In a heavy-bottomed saucepan, melt the unsalted STICK butter over medium-low heat. The melting butter will begin to form a white foam on top. This is the butter's water content boiling off.

2. Then, turn the heat to low, so the butter simmers, stirring occasionally. The froth will begin to thin slowly and the color of butter changes to a pale yellow shade.
 
3. Then, continue to cook on low heat until the butter turns a golden color. The residue of milk solids will separate from the butterfat and water at the bottom of the pot. The clarified butter, which is now clear, golden and translucent with a fragrant smell, is at the top with some foam.

4. As the butter starts to darken, immediately take it from the heat, and continue stirring.

 
5. The butter will darken in color from the residual heat. 
Continue stirring, and allow the butter and the separated milk solids to turn deep brown, much like a toasty hazelnut color. 

6. Let brown butter cool to tepid before use in the recipe, while whisking.

7. Before use, whisk again so the browned particles are suspended in the melted butter.
SARAH SAYS: Beurre noisette may be cooled to a solid form.