A neuron, the basic cell of your brain and nervous system, needs a few things to survive. One of the biggest things it needs is "activation." You see, your body is extremely efficient. That which you don't use, you lose. This is especially with nerves where, let's say, a particular neuron responsible for firing in a sequence that allows you spout off some spanish you learned for that attractive latina you had a crush on, may be fired repeatedly when you're chasing this lady; then abruptly halted after she turns you down. If we zoomed in on the neuron responsible for your spanish, we would see its connections diminish as you're no longer saying "que pasa" to the chica, and if your spanish isn't used for a very long time, that neuron responsible for your ability to speak spanish would be one of the many neurons that die every day. (If you're an adult, you've lost something like 6 neurons in the time it took you to read this first paragraph. Don't worry, you still have trillions left.)
A neuron that isn't being used will be lost. Your body is extremely resourceful, and if it sees something isn't being used, it shunts resources elsewhere.
How does this relate to your child? One of the ways neurons are activated and kept alive more than anything else is through bodily movement... through exercise! Is it any wonder why children are so full of life? They're stimulating and crafting their brains! They're doing what they were built to do. My spazz of an 11-month-old is the epitome of this: if he's awake, he's moving; if he can't move his body, he's moving his vocal chords. Nothing is still.
The best thing you can do for you kid – right up there with making sure they have enough omega-3 fatty acids – is giving them plentiful oppurtunities to move. Don't call it "exercise," because to a kid, it's fun. Just get out of the way and let them do their thing, and their brains will flourish.