That means you are able to draw on the strengths of both the right and left hemispheres of your brain, depending upon a given situation.
When you need to explain a complicated process to someone, or plan a detailed vacation, the left hemisphere of your brain, which is responsible for your ability to solve problems logically, might kick in. But if you were critiquing an art opening or coming up with an original way to file papers, the right side of your brain, which is responsible for noticing subtle details in things, might take over.
While many people have clearly dominant left- or right-brained tendencies, you are able to draw on skills from both hemispheres of your brain. This rare combination makes you a very creative and flexible thinker.
The down side to being balanced-brained is that you may sometimes feel paralyzed by indecision when the two hemispheres of your brain are competing to solve a problem in their own unique ways.