The split brain operation is designed to separate the left and right hemispheres of the brain. It is performed by sectioning through the corpus callosum, which is a fiber bundle (like a bundle of telephone wires) that its between the two hemispheres, and is easy to section without damaging the rest of the brain. The surgery is performed on people with certain forms of epilepsy, to prevent seizures from spreading thoughout the brain.
Michael Gazzaniga is responsible for much of what we know about the purpose of the corpus callosum. He has conducted psychological studies on many split brain patients. The fascinating part of his research is how little such a major surgery can affect everyday life.
However, the split brain patient demonstrates how the brain delegates certain tasks to certain sides of the brain. For example, if a split brain person covers their right eye and sees an object (a pencil) they will not be able to name that object. If they cover their other eye, they will have no problem naming items. The reason is that the left eye carries information to the right half of the brain, but the location required for naming an object sits in the left side.
Because vision is redundant in both hemispheres in humans, split brain people have no trouble naming the objects they see with both eyes. Feeling an object with the left hand and naming it would be impossible for them though.