Aerobic exercises in children have been documented to enhance cognitive ability, executive function, thought processing and neuronal viability. A few of the underlying mechanisms are as follows:

1. Regular aerobics reduce the reaction time determined through EEGs.

2. Faster cognitive processing speed assessed by p3 latency.

3. Enhances attention allocation measured by p3 amplitude.

4. Enhances cortical activation.

5. Improved speed and accuracy of thought processing.

6. Stabilised and improved controlled processing, visuospatial adaptation and orientation, stimulus evaluation, response selection, and response execution.

Above mentioned are the effects of aerobic physical activity on developing brain. However, the mechanisms bringing about these are are yet to be precisely explored.

I think this should answer you question.

Chaddock-Heyman L, Hillman CH, Cohen NJ, Kramer AF. III. The importance of physical activity and aerobic fitness for cognitive control and memory in children. Monogr Soc Res Child Dev 2014;79(4):25-50. https://pdfs.semanticscholar.org/d819/d1a994c823b9f49e995afd45b11c9853b203.pdf

Schaeffer DJ, Krafft CE, Schwarz NF, Chi L, Rodrigue AL, Pierce JE, Allison JD, Yanasak NE, Liu T, Davis CL, McDowell JE. An 8-month exercise intervention alters frontotemporal white matter integrity in overweight children. Psychophysiology 2014;51(8):728-33. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4107135/pdf/nihms600087.pdf