The Collaborative International Dictionary of English v.0.48:

Vacuum cleaner \Vac"u*um clean"er\
   A machine for cleaning carpets, tapestry, upholstered work,
   etc., by suction; -- sometimes called a vacuum.
   [Webster 1913 Suppl.]

The Collaborative International Dictionary of English v.0.48:

Appliance \Ap*pli"ance\, n.
   1. The act of applying; application.
      [1913 Webster]

   2. subservience; compliance. [Obs.] --Shak.
      [1913 Webster]

   3. A thing applied or used as a means to an end; an apparatus
      or device; as, to use various appliances; a mechanical
      appliance; a machine with its appliances.
      [1913 Webster]

   4. Specifically: An apparatus or device, usually powered
      electrically, used in homes to perform domestic functions.
      An appliance is often categorized as a major appliance or
      a minor appliance by its cost. Common major appliances are
      the refrigerator, washing machine, clothes drier,
      oven, and dishwasher. Some minor appliances are a
      toaster, vacuum cleaner or microwave oven.
      [PJC]

WordNet (r) 3.0 (2006):

vacuum cleaner
    n 1: an electrical home appliance that cleans by suction [syn:
         vacuum, vacuum cleaner]