What are the advantages of Impact Drivers?

Impact drivers provide much higher torque but in rapid bursts, similar to a hammer providing
linear bursts of force. This makes impact drivers good for heavy-duty jobs like driving long
lag bolts - you can even take the lug nuts off your car wheels with most impact drivers.
However the banging action does make them a little bit difficult to control.

Impact drivers are not suited for driving soft materials.

This is because between the hammer strikes there is no torque applied, and the bit can actually rotate backwards.
You can feel this by holding the chuck with your hands while the driver is on;
you'll feel the pulsing of the strikes but the chuck won't acually rotate.
Finally, some impact drivers do not have a clutch, which means you need to be very careful
if you're driving something that could be over-tightened or broken by the high torque.

Another clear advantage of impact drivers is that you do not have to hold them tightly
to provide the torque.
The momentum of the rotating striker inside is what provides the rotating force,
so even when you are driving something very tough it's quite easy to hold the tool.
Drills on the other hand require the user to provide the reaction and prevent the tool from spinning.