First and foremost, they offer better stopping power because the pads keep dirt and water from accumulating on the rotors.
Discs also run cooler for less fade, weigh less than drums, and are easier to service.
Also, mud and dirt can grind through drums in a matter of miles. These are strong cases for rear discs. The DOT mandates mechanically operated emergency brakes for street-legal use. The photos here provide an overview of the 14-bolt disc conversion. If attempting the swap yourself, consult a factory shop manual for proper bolt-torque specs and, if you have any doubts about the job, take it to a competent brake pro.