The Collaborative International Dictionary of English v.0.48:

Currant \Cur"rant\ (k?r"rant), n. [F. corinthe (raisins de
   Corinthe raisins of Corinth) currant (in sense 1), from the
   city of Corinth in Greece, whence, probably, the small dried
   grape (1) was first imported, the Ribes fruit (2) receiving
   the name from its resemblance to that grape.]
   [1913 Webster]
   1. A small kind of seedless raisin, imported from the Levant,
      chiefly from Zante and Cephalonia; -- used in cookery.
      [1913 Webster]

   2. The acid fruit or berry of the Ribes rubrum or common
      red currant, or of its variety, the white currant.
      [1913 Webster]

   3. (Bot.) A shrub or bush of several species of the genus
      Ribes (a genus also including the gooseberry); esp., the
      Ribes rubrum.
      [1913 Webster]

   Black currant,a shrub or bush (Ribes nigrum and Ribes
      floridum) and its black, strong-flavored, tonic fruit.

   Cherry currant, a variety of the red currant, having a
      strong, symmetrical bush and a very large berry.

   Currant borer (Zool.), the larva of an insect that bores
      into the pith and kills currant bushes; specif., the
      larvae of a small clearwing moth ([AE]geria
      tipuliformis) and a longicorn beetle (Psenocerus
      supernotatus).

   Currant worm (Zool.), an insect larva which eats the leaves
      or fruit of the currant. The most injurious are the
      currant sawfly (Nematus ventricosus), introduced from
      Europe, and the spanworm (Eufitchia ribearia). The fruit
      worms are the larva of a fly (Epochra Canadensis), and a
      spanworm (Eupithecia).

   Flowering currant, Missouri currant, a species of Ribes
      (Ribes aureum), having showy yellow flowers.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Ribes rubrum
    n 1: cultivated European current bearing small edible red
         berries [syn: red currant, garden current, Ribes
         rubrum]