The human brain is split into the left and right hemispheres. These two hemispheres are connected by a "corpus callosum" composed of approximately two hundred million nerve fibers. This bundle of nerve fibers is located right in the center of the brain and has an arch-like cross-section.
If the corpus callosum is removed, then the connection between the two brain hemispheres will be severed. In other words, if you want to study the function of just one hemisphere, you simply need to remove a person's corpus callosum to do so.
Of course, removing someone's corpus callosum just for research would be too inhumane. But there indeed exist people in the world who completely lack a corpus callosum. Among these people, a large group consists of those who suffered from epileptic seizures that could not be controlled by medical means at the time and thus had to be treated by severing the corpus callosum.
Such people without a corpus callosum are called "split-brain patients."