Try standing on one foot. Not so hard, you say? Try it with your eyes closed.
Aha! Suddenly things got much harder. With eyes closed you may begin to wobble and tilt, but as soon as you open them, things get easier again. You can achieve this same effect by standing on one foot in a completely darkened room. Don't laugh until you've tried it!
What's going on? Well, you may have heard that our sense of balance is centered in our ears. To a certain extent, this is true. In each ear is a series of organs that respond to various kinds of motion. Some sense forward and backward motion, some rotation.
These motion-detectors are not sensitive enough, however, to register movement unless it is of a fairly significant sort. You wouldn't want to get dizzy every time you turn your head!
We rely to a significant degree on our eyes for more fine-tuning of our balance. If you think about it, this makes sense. By sensing the pull of gravity or your head's motion, your ears tell you where you are. Your eyes add to that information as well, just by looking. Think of how a fast-paced movie makes you dizzy, just by watching it.
One thing some people find helps them with their eyes closed is the after-image of a bright light. Even the sensation that you are looking at something can make you feel less in danger of falling over.