The sentence you wrote is mostly correct but can be made clearer and more natural. Here's a better way to say it:
"The brain has two halves: the left side and the right side. Each half controls the opposite side of your body."
This means if you move your right hand, it is controlled by the left side of your brain. If you move your left hand, it is controlled by the right side of your brain. The two halves work together to help your body move and do many things!