The terms "left brain" and "right brain" refer to the left and right hemispheres of your brain. They each tend to process things differently, as explained in the following two paragraphs. However, the following are generalizations. They hold true for over 90% of right-handed people, and only 70% of left-handed people. In the cases where they aren't true, the division of labor and processing styles is usually still there, but reversed, with the right side handling the things that most people's left side handles, and vice-versa.
The left brain processes thing more sequentially and systematically than the right. It is more rational, or at least more logical, analytical and objective. It tends to look at the parts more than the whole. Finally, it was learned early on in studies of the hemisphere that the left side handles speech for most of us.
The right brain is the "artists" brain. It handles thing in more random and subjective manor. It is generally responsible for "hunches" and other intuitive processes. It looks more at wholes, and is best at pattern-recognition, making it the "map reading" part of the brain.
How distinct are the two halves of your brain? Consider the amazing experiments involving people who have had the corpus callosum cut. This surgery is performed on epileptics to reduce the incidence of seizures. It isolates most of the right hemisphere from the left hemisphere.
In a typical experiment, a divider lets a subject see two objects - say, a cup with the right eye and a lemon with the left. Asked what they see, they'll say "a cup," because their left brain process both language and information from the right eye. When asked to write down what they see, however, using their left hand, they'll write "a lemon," because both their left hand and eye are controlled by the right side of the brain.
The two hemispheres normally work more closely together. These split-brain experiments show how distinct the two sides really are, though. Many people think that there is some benefit to getting the two sides working better together, as they each have their strengths. Some claim that meditation accomplishes this, and there is some evidence at least for the balancing of electrical activity between the two sides during a meditative state. Alternately, you could develop whichever hemisphere seems weakest in you.
Left Brain Right Brain Dominance
You will usually favor one style or another of thinking, and this may be an indication of the dominance of either your right brain or left brain. It seems likely, for example, that the choice between joining the debating team or the art class in school would have