I would think the Glock guys would be able to explain this better than me but here goes.
In order to understand the double trigger (my term) you have to understand the striker pistol.
The striker pistol was developed to be a safe and simple police weapon, it would fire like a DA revolver with less trigger pull and travel and be as safe as a SA pistol but didn't need a safety as it was not fully cocked.
Before Striker fired pistols, most guns carried by law enforcement, when fired in the line of duty, fired from a DA mode or a cocked and locked mode, both required well trained and experienced LEO's to be good at it.
A striker gun when it is loaded by pulling back the slide and chambering a round, is also cocked but only half way. The rest of the cocking is done when the trigger is pulled and the gun then fires. After it is fired it loads the next round but it is still only half cocked, keeping the trigger pull the same for every round fired.
Glock was not the first striker fired pistol design, most say HK, some will argue that, whatever, but when Glock finished the design for it's pistol it incorporated a double trigger and no manual safety.
The double trigger was used because now that the gun was half cocked after loading it didn't need much trigger travel or other inertia to fire and brushing hard against the trigger or dropping it could possibly disccharge the gun accidently. The double trigger requires that a finger has to be fully on the trigger for the gun to fire.