The brain activity caused by exercise generates molecular by-products that can damage cells, but under normal circumstances, repair mechanisms leave cells hardier for future challenges. Neurons get broken down and built up just like muscles – stressing them makes them more resilient. This is how exercise forces the body and mind to adapt.
In Spark, The Revolutionary New Science of Exercise and the Brain, Dr. John Ratey discusses how he effects of exercise go far beyond bodily health. For example (The above quote alludes to this), exercise improves not only the brain’s conductivity and chemistry, but also its physical structure. That’s something else!