The Collaborative International Dictionary of English v.0.48:

Bay rum \Bay" rum"\
   A fragrant liquid, used for cosmetic and medicinal purposes.
   [1913 Webster]

   Note: The original bay rum, from the West Indies, is
         prepared, it is believed, by distillation from the
         leaves of the bayberry (Myrcia acris). The bay rum of
         the Pharmacop[oe]ia (spirit of myrcia) is prepared from
         oil of myrcia (bayberry), oil of orange peel, oil of
         pimento, alcohol, and water.
         [1913 Webster] Bays

WordNet (r) 3.0 (2006):

bay rum
    n 1: an aromatic liquid originally obtained by distilling the
         leaves of the bayberry tree with rum