The Collaborative International Dictionary of English v.0.48:

Near beer \Near beer\
   Any of various malt liquors (see Citation below).
   [Webster 1913 Suppl.]

         Near beer is a term of common currency used to
         designate all that class of malt liquors which contain
         so little alcohol (usually less than 1/2 per cent) that
         they will not produce intoxication, though drunk to
         excess, and includes in its meaning all malt liquors
         which are not within the purview of the general
         prohibition law.                         --Cambell v.
                                                  City of
                                                  Thomasville,
                                                  Georgia Appeal
                                                  Records, 6
                                                  212.
   [Webster 1913 Suppl.]

WordNet (r) 3.0 (2006):

near beer
    n 1: drink that resembles beer but with less than 1/2 percent
         alcohol