The Collaborative International Dictionary of English v.0.48:

Bandbox \Band"box`\ (b[a^]nd"b[o^]ks`), n.
   A light box of pasteboard or thin wood, usually cylindrical,
   for holding ruffs (the bands of the 17th century), collars,
   caps, bonnets, etc.
   [1913 Webster]

WordNet (r) 3.0 (2006):

bandbox
    n 1: a light cylindrical box for holding light articles of
         attire (especially hats)