In short, brown butter creates an intense nutty and sweet flavor that enhances just about anything you bake, sauté or you drizzle it over, especially chicken or seafood. It is a trick to get this right because there is a fine line between brown butter and BURNT butter, with the latter being disgusting. You might have a few misfires but once you master it this will become a staple of your cooking.
Take the amount of unsalter butter that you will need and put it in a sauté pan over high heat and let melt, you will see it bubble and then brown. At the same time prepare a bowl to pour the butter in and add 10% of refrigerated butter to the bowl. So for every stick of butter that you brown, add an additional teaspoon of butter to the bow.
You should stir with a wooden spoon to scrape up the brown bits until it is brown but not black, that is a big difference in the flavor profile, pour the melted butter into the bowl with the still cold butter and watch it bubble.