The Collaborative International Dictionary of English v.0.48:

Allspice \All"spice`\, n.
   The berry of the pimento (Eugenia pimenta), a tree of the
   West Indies; a spice of a mildly pungent taste, and agreeably
   aromatic; Jamaica pepper; pimento. It has been supposed to
   combine the flavor of cinnamon, nutmegs, and cloves; and
   hence the name. The name is also given to other aromatic
   shrubs; as, the Carolina allspice (Calycanthus floridus);
   wild allspice (Lindera benzoin), called also spicebush,
   spicewood, and feverbush.
   [1913 Webster]

WordNet (r) 3.0 (2006):

allspice
    n 1: aromatic West Indian tree that produces allspice berries
         [syn: allspice, allspice tree, pimento tree, Pimenta
         dioica]
    2: deciduous shrubs having aromatic bark; eastern China;
       southwestern and eastern United States
    3: ground dried berrylike fruit of a West Indian allspice tree;
       suggesting combined flavors of cinnamon and nutmeg and cloves