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.
      [1913 Webster]

   2. The woman who is in charge of a household.
      [PJC]

   3. The woman who is in charge of a brothel.
      [PJC]