Everything is explained in "Harry Potter and the Secrets of Arduino PWM".
The driver by itself do not include the dimming function, but you can still add it yourself easily. You can also use a driver compatible with PWM, in this case you may be able to plug it directly to the arduino without mosfet but it may be messy as I use a 3.3V logic arduino for the radio. It's also cheaper to do it yourself and in my case easier to wire.
Both LED and Fan outputs are controlled by a mosfet linked to a PWM pin of the arduino (pin 5-6). Mosfets (power transistors) behave like a switch: when the arduino send some current to the gate, the switch is closed -> light on.
Dimming effect is performed by "switching on and off" the light faster than your eye can see it, resulting in a dim light level depending on the time ratio ON:OFF. Input power is always either 34V/1750mA or 0V/0mA but if you are using a multimeter you will detect a lower voltage. An oscilloscope will show you a square wave 0V/34V.
This on/off cycle is why in many LEDs, when dimmed to a low level, you may see a flicker in the light. Frequency is low enough for you to "see" the on/off cycle.
Doing that with an incandescent light, or CFL, would damage it in no time, but LEDs are perfect for this. That's what is used in any LED dimming appliance, bulb or other, I did not invent anything at all. No magic or anything fancy, totally safe and won't damage the LED or the driver.