Perhaps this expression is more literal than we thought –

       Here’s what it means:

Being in motion makes us smarter, and being smarter allows us to move more efficiently.

       Here’s the scientific hypothesis:

Jogging after prey helped to drive human brain evolution.  A million years ago, we could out-run and out-walk most other mammals over long distances. Our brains were shaped and sharpened by movement. We continue to require regular physical activity in order for our brains to function optimally.

      There are many studies.

http://well.blogs.nytimes.com/2012/12/26/exercise-and-the-ever-smarter-human-brain/?_php=true&_type=blogs&_r=0 

       Here’s a finding:

Regular exercise, even walking, leads to more robust mental abilities, beginning in childhood and continuing into old age.

Picture source:  http://www.123rf.com/stock-photo/jogger.html