Plato (429-348 BC): Brain is responsible for mental activities.
Hippocrates 400 BC: Brain controls the senses and movement.
But Aristotle believed that the brain cooled the blood and that the heart was the locus of thought and sensation. Aristotle's ideas too survived through the Middle Ages.
Specificity of brain function: Descartes recognised that different parts of the brain control different bodily functions - located the interaction between the soul and the body at the pineal gland at the base of the brain. His contemporary Juan Huarte suggested instead that the brain works as a unit.
Proposal for functional decomposition of the brain: Franz Joseph Gall (1758-1828): In the early 19th C suggested that mental and character traits could be correlated with independent ``organs'' of the brain which in turn showed up as protrusions and indentations in the skull. Although this ``phrenology'' was later throughly discredited, Gall's claim about structural and a corresponding functional differentiation of the brain cortex came to be widely accepted. (Also made many other important discoveries in neuroscience)
Discovery of lateralization of motor function led to support for localization of function.