Brain development
Some of the most important physical developments occurring during this age range are occurring in the brain. By 3 years old, the brain is around 75% of its adult size and by 5 years old, it has reached 90% of its adult size.
Over this age range the nerves develop a fatty cover, or myelin sheath which increases the speed at which they can transmit messages. This increase in speed allows the child to develop their cognitive and motor abilities and skills and enables them to develop the greater concentration and focus necessary for learning.
For example, when the child learns to read, the visual cues from a sequence of letters is transmitted to the visual cortex at the back of the brain and from there to the part of the brain that processes and translates the information received. Finally the information is sent to areas that are able to process this information into speech to enable the child to articulate the words seen. This involves a massive amount of information transfer by nerves and this simply wouldn't happen fast enough without myelination.
Contemporary neuroscience suggests that different areas of the brain are highly specialised for different functions, for example for language, logic, creativity, maths, intuition etc. This is known as lateralisation. Whilst there is some fluidity in the areas that can perform these functions in younger children, during this age areas become more specialised, although degrees of fluidity do exist throughout life.