A dimmer switch can cause a light bulb's filament to vibrate, making a buzzing sound when its on a less-than-full setting. You can buy a new dimmer that's designed not to buzz and replace the switch, but before you do, try replacing the bulb with a "long life" light bulb that has a sturdier filament and is rated 130 volts instead of the far more common 120 volts.

For more about wiring techniques, see How to Wire a Dimmer Switch.