The Collaborative International Dictionary of English v.0.48:

Derby \Der"by\ (?; usually ? in Eng.; 85), n.
   1. A race for three-old horses, run annually at Epsom (near
      London), for the Derby stakes. It was instituted by the
      12th Earl of Derby, in 1780.
      [1913 Webster]

   Derby Day, the day of the annual race for the Derby stakes,
      -- Wednesday of the week before Whitsuntide.
      [1913 Webster]

   2. A stiff felt hat with a dome-shaped crown.
      [1913 Webster]

WordNet (r) 3.0 (2006):

derby
    n 1: a felt hat that is round and hard with a narrow brim [syn:
         bowler hat, bowler, derby hat, derby, plug hat]