Real Dictionary

madam
vocative noun: People sometimes say Madam as a very formal and polite way of addressing a woman whose name they do not know or a woman of superior rank. For example, a shop assistant might address a woman customer as Madam.

madam in American English
a woman; lady
noun: a polite term of address to a woman, originally used only to a woman of rank or authority

madam in British English
noun: a polite term of address for a woman, esp one considered to be of relatively high social status