The Collaborative International Dictionary of English v.0.48:

Basidium \Ba*sid"i*um\, n. [NL., dim. of Gr. ba`sis base.]
   (Bot.)
   A special oblong or pyriform cell, with slender branches,
   which bears the spores in that division of fungi called
   Basidiomycetes, of which the common mushroom is an example.
   [1913 Webster]

WordNet (r) 3.0 (2006):

basidium
    n 1: a small club-shaped structure typically bearing four
         basidiospores at the ends of minute projections; unique to
         basidiomycetes