This is a great, accessible review of the literature supporting the view that aerobic exercise has positive effects on the growth and development of the brain.
Also see: Athletic Mice Have Bigger (mid) Brains
Linking brains and brawn: exercise and the evolution of human neurobiology
The hunting and gathering lifestyle adopted by human ancestors around 2 Ma required a large increase in aerobic activity. High levels of physical activity altered the shape of the human body, enabling access to new food resources (e.g. animal protein) in a changing environment. Recent experimental work provides strong evidence that both acute bouts of exercise and long-term exercise training increase the size of brain components and improve cognitive performance in humans and other taxa. However, to date, researchers have not explored the possibility that the increases in aerobic capacity and physical activity that occurred during human evolution directly influenced the human brain. Here, we hypothesize that proximate mechanisms linking physical activity and neurobiology in living species may help to explain changes in brain size and cognitive function during human evolution. We review evidence that selection acting on endurance increased baseline neurotrophin and growth factor signalling (compounds responsible for both brain growth and for metabolic regulation during exercise) in some mammals, which in turn led to increased overall brain growth and development. This hypothesis suggests that a significant portion of human neurobiology evolved due to selection acting on features unrelated to cognitive performance.