The Collaborative International Dictionary of English v.0.48:
Madam \Mad"am\, n.; pl. Madams, or Mesdames. [See Madame.]
1. A gentlewoman; -- an appellation or courteous form of
address given to a lady, especially an elderly or a
married lady; -- much used in the address, at the
beginning of a letter, to a woman. The corresponding word
in addressing a man is Sir; often abbreviated ma'am when
used as a term of address.
2. The woman who is in charge of a household.
3. The woman who is in charge of a brothel.