madam

The definition of madam is a respectful title for a woman, or a woman who runs a house of prostitution.

(noun)

When you want to greet a woman formally who has just arrived at your restaurant for brunch, this is an example of a time when you might say "Good morning madam."
When you are writing a formal business letter to a woman from whom you are trying to solicit business, this is an example of a situation where you might say "Dear Madam."
A woman who is running a brothel where prostitutes work for money is an example of a madam.

See madam in Webster's New World College Dictionary

noun pl. madams

Origin: Fr madame, orig. ma dame < L mea domina, my lady: see dame

See madam in American Heritage Dictionary 4

noun Abbr. Mdm.

pl. Mes·dames (mā-dămˈ, -dämˈ) Used formerly as a courtesy title before a woman's given name but now used only before a surname or title indicating rank or office: Madam Ambassador.
Used as a salutation in a letter: Dear Madam or Sir.
madam Used as a form of polite address for a woman: Right this way, madam.
madam The mistress of a household.
madam A woman who manages a brothel. See Usage Note at mistress.