The Collaborative International Dictionary of English v.0.48:

Burgher \Burgh"er\, n. [From burgh; akin to D. burger, G.
   b["u]rger, Dan. borger, Sw. borgare. See Burgh.]
   1. A freeman of a burgh or borough, entitled to enjoy the
      privileges of the place; any inhabitant of a borough.
      [1913 Webster]

   2. (Eccl. Hist.) A member of that party, among the Scotch
      seceders, which asserted the lawfulness of the burgess
      oath (in which burgesses profess "the true religion
      professed within the realm"), the opposite party being
      called antiburghers.
      [1913 Webster]

   Note: These parties arose among the Presbyterians of
         Scotland, in 1747, and in 1820 reunited under the name
         of the "United Associate Synod of the Secession
         Church."
         [1913 Webster]

WordNet (r) 3.0 (2006):

burgher
    n 1: a citizen of an English borough [syn: burgess, burgher]
    2: a member of the middle class [syn: bourgeois, burgher]

Moby Thesaurus II by Grady Ward, 1.0:

51 Moby Thesaurus words for "burgher":
   Babbitt, Christian, Middle American, Philistine, anal character,
   big-city man, bourgeois, burgess, citizen, city dweller, city man,
   city slicker, compulsive character, conformer, conformist,
   conventionalist, exemplary citizen, exurbanite, formalist,
   good citizen, good neighbor, methodologist, middle-class type,
   model child, oppidan, organization man, parrot, pedant,
   perfectionist, pillar of society, plastic person, precisian,
   precisianist, respectable citizen, sheep, square, suburbanite,
   teenybopper, townee, towner, townfolk, townfolks, townsman,
   townspeople, townswoman, trimmer, true Christian, urbanite,
   villager, villageress, yes-man