The connection between movement and the brain has recently been scientifically established . A good breakdown can be found in the book "Spark: The Revolutionary New Science of Exercise and the Brain Paperback – January 1, 2013 by John J. Ratey"
Basically movement, especially aerobic (walk, run, etc.) but also complex movement (sports, music playing , martial arts) as explained in the book
1 causes neurogenesis (release of brain stem cells ) 2 increases the size of your hippocampus and and improves memory 3 creates new brain circuits for the movement but these circuits are able to be recruited by different tasks 4 increases the production and balance of neurotransmitters and other hormones 5 increases and regulates executive function And a lot more complex processes in the brain. This occurs immediately but increases with more exercise . It's interesting stuff and ratey explains well.