Running helps counteract the negative effects of stress on the hippocampus, the part of the brain responsible for learning and memory.
news.byu.edu
This study was done in mice and found that mice that were exposed to stress had a decrease in long-term potentiation in the hippocampus. Long-term potentiation is the process that helps solidify the connections between neurons during memory formation. When animals were stressed but were also forced to run on a wheel, they did not experience a decrease in long-term potentiation.
Brief bursts of norepinephrine are released during exercise have been shown to increase long-term potentiation which has long-term benefits on cognition and is very relevant for brain aging.