Madam \Mad"am\, n.; pl. Madams, or Mesdames. [See Madame.]

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.

Source: Webster's Revised Unabridged Dictionary (1913)