Xabu, welcome to TFF! There is no such thing as a dumb question if you don't know the answer to it. The only "dumb" people are the ones who don't ask questions when they don't know.
The others here have the right of it. The part you circled is, of course, the thumb safety for the weapon. It won't engage unless the hammer is fully cocked. When the weapon is carried with the hammer cocked, a round in the chamber, and the thumb safety engaged it is in what we call "Condition One," i.e., to fire all that is needed is for the thumb safety to be disengaged by your thumb while the butt safety is pressed down by your grip on the pistol butt. Pressing the trigger will then dicharge the weapon. "Condition Two" is similar except that the hammer is carried in the down position with a live round in the chamber and a full magazine is in place, thus the hammer must be pulled completely back to the cocked position by the thumb in order to discharge the weapon. In Condition Two, the thumb safety is, of course, not engaged at all. You effectively have simple single action operation, not unlike what occurrs in a single-action revolver. The only danger with Condition Two is that it is conceivable that the weapon could accidentally discharge if dropped directly on the hammer from a height of several feet. It's not likely, but it can happen. Condition Three is when the weapon is carried with a full magazine, hammer down, but NO round in the chamber. To fire, it is necessary first actually to cock the slide to put a round in the chamber, which normally takes two hands. This is the safest way to carry a single action auto, and the manner offically specified in the military, not that most of us carried it that way.
I too have a Llama IIIA and I can confirm it breaks down and reassembles virtually identically to a 1911 pattern .45 pistol.