The Collaborative International Dictionary of English v.0.48:

Gymnasium \Gym*na"si*um\ (j[i^]m*n[=a]"z[i^]*[u^]m or
   j[i^]m*n[=a]"zh[i^]*[u^]m; 277) n.; pl. E. Gymnasiums
   (j[i^]m*n[=a]"z[i^]*[u^]mz), L. Gymnasia
   (j[i^]m*n[=a]"z[i^]*[.a]). [L., fr. Gr. gymna`sion, fr.
   gymna`zein to exercise (naked), fr. gymo`s naked.]
   1. A place or building where athletic exercises are
      performed; a school for gymnastics.
      [1913 Webster]

   2. A school for the higher branches of literature and
      science; a preparatory school for the university; -- used
      esp. of German schools of this kind.
      [1913 Webster]

            More like ordinary schools of gymnasia than
            universities.                         --Hallam.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Gymnasium
    n 1: a school for students intermediate between elementary
         school and college; usually grades 9 to 12 [syn: secondary
         school, lyceum, lycee, Gymnasium, middle school]
    2: athletic facility equipped for sports or physical training
       [syn: gymnasium, gym]