The Collaborative International Dictionary of English v.0.48:

Buckeye \Buck"eye`\ (b[u^]k"[imac]`), n.
   1. (Bot.) A name given to several American trees and shrubs
      of the same genus ([AE]sculus) as the horse chestnut.
      [1913 Webster]

   The Ohio buckeye, or Fetid buckeye, is Aesculus glabra.


   Red buckeye is Aesculus Pavia.

   Small buckeye is Aesculus paviflora.

   Sweet buckeye, or Yellow buckeye, is Aesculus flava.
      [1913 Webster]

   2. A cant name for a native or resident of Ohio. [U.S.]
      [1913 Webster]

   Buckeye State, Ohio; -- so called because buckeye trees
      abound there.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Buckeye State
    n 1: a midwestern state in north central United States in the
         Great Lakes region [syn: Ohio, Buckeye State, OH]