You might think that only brain activities makes you smarter, but this is not the case as scientists point out. The brain is relatively small to the overall body weight, about 2% of it, but it is a huge nutrient consuming machine. It also consumes up to 1/3 of the oxygen breathed in. Physical exercise causes extra oxygen to flow through the veins into the brain, as well as nutrients. Scientists think that this may help stimulate the production of new nerve cells in the hippocampus, a process called Neurogenesis. These extra neurons add-up and become part of scientists call "brain reserve".
Physical exercise not only helps you build a more intelligent personality, but it also helps people with brain damages. A study among old ladies between 70 and 80 years old showed that regular exercise increased the brain process speed.
Old Greeks had many sayings to point the importance of physical and mental exercise like the well known "Healthy mind in healthy body" [Greek] which means that for a healthy mind one must have a healthy body.