Research has shown that listening to music works more areas of the brain than any other activity humans can do. However, playing music works even more areas than simply listening to it.
What is it about making music that does this? Playing an instrument engages practically every area of the brain at once, most notably the visual, auditory, and motor cortices.
The most obvious difference between listening to music and playing it is that the latter requires fine motor skills which are controlled in both hemispheres of the brain. It also combines the linguistic and mathematical precision in which the left hemisphere is more involved with the novel and creative content that the right excels in.
For these reasons, playing music has been found to increase the volume and activity in the brains corpus callosum – the bridge between the two hemispheres – allowing messages to get across the brain faster and through more diverse routes. This may allow musicians to solve problems more effectively and creatively in both academic and social settings.
As with any activity that you do, disciplined, structured practice strengthens those brain functions that are utilized in that activity. However, the strength doesn't just re-apply itself to that single task, but it allows us to apply that strength to other activities as well.
As kids are going back to school their schedules will become busier, I encourage everyone to set aside time to practice every day – from 20 minutes at a minimum, up to 1 hour per day for the more serious student. The time invested in practicing their instrument will not take away from other activities, but enhance them dramatically.
For those that would like to learn more on this topic I highly recommend reading the book "This Is Your Brain on Music" by Daniel J. Levitin.