The Collaborative International Dictionary of English v.0.48:

Tenement \Ten"e*ment\, n. [OF. tenement a holding, a fief, F.
   t[`e]nement, LL. tenementum, fr. L. tenere to hold. See
   Tenant.]
   1. (Feud. Law) That which is held of another by service;
      property which one holds of a lord or proprietor in
      consideration of some military or pecuniary service; fief;
      fee.
      [1913 Webster]

   2. (Common Law) Any species of permanent property that may be
      held, so as to create a tenancy, as lands, houses, rents,
      commons, an office, an advowson, a franchise, a right of
      common, a peerage, and the like; -- called also free
      tenements or frank tenements.
      [1913 Webster]

            The thing held is a tenement, the possessor of it a
            "tenant," and the manner of possession is called
            "tenure."                             --Blackstone.
      [1913 Webster]

   3. A dwelling house; a building for a habitation; also, an
      apartment, or suite of rooms, in a building, used by one
      family; often, a house erected to be rented.
      [1913 Webster]

   4. Fig.: Dwelling; abode; habitation.
      [1913 Webster]

            Who has informed us that a rational soul can inhabit
            no tenement, unless it has just such a sort of
            frontispiece?                         --Locke.
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   5. A tenement house.
      [PJC]

   Tenement house, commonly, a dwelling house erected for the
      purpose of being rented, and divided into separate
      apartments or tenements for families. The term is often
      applied to apartment houses occupied by poor families,
      often overcrowded and in poor condition.
      [1913 Webster +PJC]

   Syn: House; dwelling; habitation.

   Usage: Tenement, House. There may be many houses under
          one roof, but they are completely separated from each
          other by party walls. A tenement may be detached by
          itself, or it may be part of a house divided off for
          the use of a family. In modern usage, a tenement or
          tenement house most commonly refers to the meaning
          given for tenement house, above.
          [1913 Webster +PJC]

WordNet (r) 3.0 (2006):

tenement house
    n 1: a run-down apartment house barely meeting minimal standards
         [syn: tenement, tenement house]