In French cooking the precious juicy goodness left in a pan after browning meat is called a fond. In French fond means "base," and the fond is indeed the base of many sauces. After the grease is poured off these crispy bits of flavor are cooked with aromatics, wine or stock. The most recent Cooks Illustrated recommends using a stainless steel pan versus a nonstick or cast iron when browning meat and creating a fond.
The picture above is from Cooking for Engineers' recipe for Beef Stroganoff, where browning the meat with the onions for some time imparts a deeper, stronger flavor to the sauce.