|MadSci Network: Neuroscience|
Humans are bilateral for a reason. As we grow into a fetus, and later into a baby, both sides of our body develop at the same time. Later on, these two halves are joined, which is the source of many "seam-like" parts of your body, most visibly the divot under your nose and the flap of skin under your tongue.
So it was with your brain. It developed both halves simultaneously and then was joined at the center by a series of connecting neurons called the corpus callosum. It is this network that allows the two halves of the brain to communicate with each other.
In recent usage, it has become popular to refer to anything analytical as "left-brained" and anything creative as "right-brained". There is evidence to suggest that the left half deals more with speech and writing, while the right half holds colors and shapes. For example, if you held a ball in your hands, your left half would know the word "ball" while the right half would know the color. Size, elasticity, and other complex properties probably fall somewhere in between. That's probably the limit of the division between them, though. Things like analysis and creativity require both halves of the brain.
Moderator's Note: this division of knowledge is only evidenced in split-brain studies where the corpus callosum is severed.
Try the links in the MadSci Library for more information on Neuroscience.