Source : Webster's Revised Unabridged Dictionary (1913)

Near beer \Near beer\
   Any of various malt liquors (see Citation).

         Near beer is a term of common currency used to
         designate all that class of malt liquors which contain
         so little alcohol 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.

Source : WordNet®

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