Atendency for the brain's left and right hemispheres to serve different functions is called

Lateralization

Explanation:

Lateralization is the tendency of brain's left and right hemispheres to have different functions. The two hemispheres are separated by medial longitudinal fissure and are connected via corpus callosum.

The two hemispheres serve different functions because of different type of neural network arrangement. For example,  Broca's and Wernicke's areas are found in left hemisphere and they are responsible for producing and understanding speech. Damage to either side can effect the body function controlled by that part. For example, right hemisphere damage can result in lack of emotional intonation while speaking. They might also have difficulty perceiving big picture aspects of an image.

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