The Collaborative International Dictionary of English v.0.48:

Podesta \Po*des"ta\, n. [It. podest[`a], fr. L. potestas power,
   magistracy. See Potent.]
   [1913 Webster]
   1. One of the chief magistrates of the Italian republics in
      the Middle Ages. --Brande & C.
      [1913 Webster]

   2. A mayor, alderman, or other magistrate, in some towns of
      Italy.
      [1913 Webster]