There are lots of reasons why regular aerobic exercise is good for the brain - the effects of exercise on brain volume, cognition and mood are profound and enduring.
In an early review paper, Colcombe and Kramer (2003) conducted a meta-analysis of 18 interventional studies, conducted over a 25-year period. Their general conclusion was that fitness training in the elderly increased performance by approximately .5 of a standard deviation across all tasks tested. Maximal effects were found for tasks related to executive functions, (i.e., aspects of higher cognition principally associated with the functions of prefrontal cortex).
The next greatest set of effects were found for cognitive functions associated with the transition from effortful learning to automatic processing (i.e. tasks such as driving, that demand concentration and attention during their learning and execution, but which through practice become more automatic).
The next greatest effect was on visuo-spatial factors (i.e., factors associated with visualising and interacting with the three-dimensional world).