Brown sauce is Sauce Espagnole. It is made by making a brown roux.
Butter or oil and flour cooked till it is a nice nut brown, and browning beef or veal with bones in the oven, and adding the roux and brown meat and bones to a pot of water and onion, carrot, garlic, parsley, thyme, bayleaf, salt and pepper, tomato paste, and simmering for several hours. it is usually used as the base for some other sauce- like chile. Or you can go to the grocery store and buy the stuff in a can.
Or you can buy The Joy of Cooking (not to be confused with the Joy of Sex which you might also want to buy) and Erma will tell you more about Brown Sauce than you will ever want to know.