The brain contains a lot of hardwiring. There's a lot of everyday functions and movements, such as reflexes, that we use everyday without thinking.
For example most of us don't give much though to how we use our eyes day to day. Our head can turn while we are looking at something in front of us, and our eyes will remain fixed on whatever we were looking at with no conscious effort at all.
The reflex mentioned above is called an oculocephalic reflex, which describes how the eyes automatically adjust for changes in head position. When the head turns, the eyes automatically tend to move the opposite direction. The inner ear captures the sense of motion and relays a message to the eye muscles. All of this happens within the brainstem, one of the most basic structures in our nervous system. The result is a rhythmic jerking of the eyes called nystagmus.
Often nystagmus is normal. If you watch passengers on a train, you can quickly see what nystagmus looks like by watching someone looking out of the train window. Their eyes very quickly move to one side then back to center as they track the world rushing by. This phenomenon is known as optokinetic nystagmus. It's the result of an automatic mechanism for tracking objects in motion.
Brainstem reflexes are not only helpful in day-to-day life, but they can also clue a neurologist into whether there is a problem with the nervous system. In vertigo, for example, a person may feel like they are spinning in a circle. Sometimes this is due to a problem with the inner ear. Due to faulty signaling in the brainstem, not only does a person feel like they're whirling in a circle, the reflex that would normally move their eyes appropriately is firing off as well. Side-to-side eye movement (horizontal nystagmus) is the result.
Depending on how the nystagmus looks, neurologists may be able to tell more about where problems lurk in the nervous system. For example, nystagmus that doesn't die down after a few seconds is more likely to come not from the inner ear, but a problem with the brainstem itself. Nystagmus that goes up and down (vertical nystagmus) is another ominous sign of brainstem disease like a intracerebral hemorrhage.
As part of the physical examination, when someone is dizzy, neurologists will watch eye movements very closely, and may even move the patient's head around to see how the eyes respond. This is all part of ensuring that the mechanisms that keep us coordinated are functioning properly.