used without a name as a form of respectful address to a woman, sometimes used obliquely

Will madam have the fish?

(Madam) used with Dear as a conventional form of address at the beginning of a letter

(Madam) used in direct address as a conventional title of respect before a woman's title of office

Madam Chairman

the female head of a brothel

Brit, informal a conceited or petulant young lady or girl