The noun HEMISPHERE has 3 senses: 1. half of the terrestrial globe. 2. half of a sphere. 3. either half of the cerebrum. Familiarity information: HEMISPHERE used as a noun is uncommon.eft brain; left hemisphere (the cerebral hemisphere to the left of the corpus callosum that controls the right half of the body). right brain; right hemisphere (the cerebral hemisphere to the right of the corpus callosum that controls the left half of the body).