The right and left sides of the brain are equally important. Both sides, called hemispheres, have different functions, but signals constantly travel back and forth between the two via the corpus callosum. The latter is a large bundle of nerve fibers that helps with functions such as stereoscopic vision.
The right hemisphere is considered the creative side because it helps to process music, visualize images and interpret language context and tone. While it doesn't perform mathematical calculations, it does help with size comparisons of different objects. The left brain, considered the analytical side, controls logic, speech and mathematical applications. It is also in charge of retrieving facts from the memory center when needed.
The brain and body are also cross wired. The right side of the brain controls the left side of the body and the left hemisphere, the right side. When people suffer a stroke in the right hemisphere, the left side of the body is affected. That doesn't mean that if someone is right-handed they are left-brained. Scientists are still working on that part of the puzzle.
The harmonious relationship between the left and right hemispheres is known as brain asymmetry. As described by Professor Stephen Wilson from the University of London, it allows both hemispheres to become specialized, but doesn't let them work independently.