Neurologically speaking, the LEFT hand is actually the one at the end of the RIGHT arm.
As a general rule, each cerebral hemisphere controls the opposite side of the body; things on the left half of the body are controlled by the right side of the brain and vice-versa. Biology is complicated,[citation needed] of course, so as with most biology "rules" there are exceptions, such as the cranial nerves, but it's true for most motor functions, if not strictly correct in all cases.
Randall spoofs this by saying that rather than controlling the left half of the body, the right brain controls the top. This Euler-diagram-like picture echoes maps that display a territorial dispute, suggesting that the halves of your brain fight for control of the region, or "dual control" like in an airplane, where the pilot and the copilot both can control the plane at any time. The reorganization also leaves a gap in the bottom left, implying that the left leg is not controlled by any part of the brain, and instead has a mind of its own.
The title text proposes that the hands should be referred to not by their physical location, but by the hemisphere of the brain they're connected to. Of course, this is not only silly but inconsistent: if the hands were labelled by hemispheres of the brain, the same would presumably apply to the arms. Furthermore, there would be no reason to give left/right names to the hemispheres themselves, since their placement in the skull would be irrelevant.