The left side of your brain controls the muscles on the right side of your body, and it is responsible for language along with logical and mathematical thinking. Meanwhile, the right brain controls the muscles on the left side of your body, and it is associated with spatial reasoning and musical abilities.
Scientists call functions that are dominated by one hemisphere of the brain "lateralized." While the left hemisphere of the brain is specialized for functions like language and mathematical thinking, the right hemisphere also works on these functions to a lesser degree. Scientists primarily determine where brain functions are localized and lateralized through a method called "experimental ablation" in which parts of the brain are selectively damaged; when a function is hampered by damage to a specific area of the brain, it becomes evident that the function in question is performed by that area.
This practice is highly unethical in human subjects, so neuroscientists must rely on clinical studies of people who already have brain damage to determine the localization and lateralization of brain function. One famous case of this that helped elucidate the function of the left brain involved a patient studied by French neurologist Paul Broca. This patient was not physically mute, and he understood language. However, he could not speak or write. Upon autopsy after that patient's death, Broca found that a part of his left brain, now called Broca's area, was damaged. A similar process led to the understanding of a related area in the left brain called Wernicke's area. Patients who have suffered damage to Wernicke's area can speak, but they often speak in ways that do not make sense. They also have trouble understanding language. From clinical studies like these, scientists have determined that most parts of language are carried out by specific areas in the left brain. Similar findings have shown scientists that the left hemisphere of the brain is responsible for mathematical and logical thinking as well as control of the right side of the body.