The following excerpt from an article titled "Notes On Set Triggers" illustrates a typical double set trigger assembly, and describes its purpose and operation. The article is from the December, 1928 issue of the "American Rifleman" magazine.
Figure 1 in the article above uses a cross-hatched circle as a cross-sectional representation of the sear arm of a gun lock. The following photo of a percussion lock identifies the sear arm, which projects from the tail of the sear. The photo has been mirror-imaged to match the orientation of the trigger assembly in Figure 1. When the trigger assembly lifts the sear arm, the hammer of the gun "falls" (i.e., rotates) and detonates a percussion cap (not shown) which fires the gun. For a non-mirrored photos of both sides of the lock, click here. For an illustrated description of the basic internal mechanism of a gun lock, click here.
The following image, which is from the February, 1944 issue of the "Muzzle Blasts" magazine, illustrates the same type of set trigger assembly that is represented by Figure 1 of the "American Rifleman" article. In the 1944 image, all surfaces of the trigger assembly have been polished, which is not typical. The caption of the 1944 image reflects this, stating “Especially Fine Triggers by E. L. Milam, Manual Training Teacher, Amateur Gunsmith (Currently in U. S. Navy).”