The Collaborative International Dictionary of English v.0.48:

left brain \left" brain`\, n.
   The left cerebral hemisphere of the brain; in humans, it
   controls motor activity on the right side of the body, and in
   most people is the primary location for control of language,
   logic, and mathematical thought.
   [PJC]

WordNet (r) 3.0 (2006):

left brain
    n 1: the cerebral hemisphere to the left of the corpus callosum
         that controls the right half of the body [syn: left
         hemisphere, left brain]