The narrator uses a near-parody of the "youtube voice" to explain what happens when the bundle of neural fibers (corpus callosum) connecting the left and right hemispheres of a person's brain is severed. The hemispheres will operate independently of each other, sometimes in an adversarial way. For example, when the right brain (which is less verbal than the left brain) is given a written instruction, the person reacts appropriately, but the left brain won't know why the person followed the instruction, and will make up a reason for performing the action.
Here's a video about a man who had his corpus callosum severed to treat his epilepsy. He said he doesn't feel different but experiments reveal unusual behavior.