The Collaborative International Dictionary of English v.0.48:

Variety show \Variety show\
   A stage entertainment, live or televised, of successive
   separate performances, usually songs, dances, acrobatic
   feats, dramatic sketches, exhibitions of trained animals, or
   any specialties. When performed live in a theater, it was
   often called a vaudeville show, but when television became
   a dominant form of entertainment live vaudeville performances
   almost completely ceased.
   [Webster 1913 Suppl. +PJC]

WordNet (r) 3.0 (2006):

variety show
    n 1: a show consisting of a series of short unrelated
         performances [syn: variety show, variety]