Light dimmers are circular switches that turn. They work by adjusting the voltage that is being sent to the light. Less voltage means that the light bulbs will shine less brightly.
Light dimmers do not know what they are connected to, they only regulate voltage. Therefore, they can work on ceiling fans and not only dim the lights on the ceiling fan but adjust the speed of the fan. On the negative side, light dimmers can switch off or half cycle in response to a surge of voltage on the same circuit. This could possibly damage the fan.
While light dimmers can work to control a ceiling fan there are dimmers made specifically for fans. They are called fan dimmers or electronic fan speed controls. They cost slightly more than the light dimmers, but are designed for ceiling fans.