In Quigley Down Under (1990) there is a scene where Quigley displays his capabilities of long range shooting with his rifle by shooting a bucket. In the scene, Quigley describes his weapon.
Marston: The legendary Sharp.
Quigley: You know your weapons. It's a lever-action breech loader. Usual barrel length's 30 inches. This one has an extra four. It's converted to use a special .45-caliber, 110-grain metal cartridge with a 540-grain paper-patched bullet. It's fitted with double set triggers and a vernier sight. It's marked up to 1200 yards. This one shoots a mite further.
The scene in question can be viewed on youtube:
So what exactly is the purpose of the double set triggers?