Final answer:
The deep groove between the right and left cerebral hemispheres is called the longitudinal fissure, which separates the brain into two distinct hemispheres connected by the corpus callosum.
Step-by-step explanation:
The very deep groove that runs between the right and left cerebral hemispheres is called the longitudinal fissure. This prominent feature of the brain's surface separates the brain into two halves or hemispheres: the right hemisphere and the left hemisphere.
These two hemispheres are connected by the corpus callosum, a thick bundle of nerve fibers that serves as the main avenue for communication between the hemispheres. The longitudinal fissure is a large separation that is vital for neurological functions and the organization of the brain's cerebral cortex.