Mens sana in corpore sano
Roughly translated, the above latin quotation by Juvenal means that those who have a healthy body will have a healthy mind.
It is now known that when a person exercises, their brains produce a quantity of a chemical called "brain derived neurotrophic factor" or BDF. This chemical acts like fertilizer on brain cells causing them to sprout branches and grow like crazy.
Animal trials using rats and mice divided into an exercising group with access to wheels, and those who led more sedentary lives found that the exercising animals learned far more quickly than their couch potatoe counterparts. Upon dissection it was found that not only was the athletic rodents bodies more buff, so was their brains. They had more neurons, and greater connectivity, which is a sign of learning ability.
In addition to improving your brain's ability to work, there is heavy evidence that those who exercise are less likely to develop Alzheimer's or Parkinson's diseases.
So now I have another good reason to continue walking and running on my elliptical trainer.