I would comment - in addition to
@MistWolf ’s design description above - that not all two stage triggers share the same design philosophy for application.
You’ll commonly see two camps (or 3-ish) of two-stage triggers, largely designed for two different purposes - precision shooting vs. tactical shooting. One camp has a light take-up (first stage, slack) with a heavy break (second stage), whereas the other camp has a heavier take-up with a light break. The 3rd camp, personally I lump in with the first - triggers with roughly the same weight for each stage - call it “1B”.
1) Light/Heavy: A Savage accutrigger or the Glock/striker pistol trigger block safety are familiar proxies for most people to the latter camp. The first stage is light so a shooter can get their finger on the trigger with increased safety, and then hold against a heavier wall to deliver the break. The Rock River NM and Varmint triggers are an example of this - 1/2lb slack plus a 4-4.5 or 3-3.5lb second stage, respectively. So the shooter gets their finger on the trigger and takes up slack, but basically the trigger feels like a single stage. You are kinda just pushing the first stage out of the way, pushing it up against a wall, before you run into the actual trigger. Personally, I consider this effectively equivalent to a single stage, but with added (unnecessary) safety, by increased sear engagement and pretravel (creep). Such, I personally consider these “tactical 2 stage triggers,” meaning they offer increased security and increased feedback for trigger sensation to a shooter with other things on their mind - but they really don’t offer additional stability during the break, as the second stage break weight is basically the same as a single stage break could have been, with less take-up.
1B) Mid/Mid: Triggers like the Larue MBT-2s are effectively balanced. You’re still going to run into a fairly heavy second stage wall, but the first stage is heavier getting there. Your finger can find the trigger and start a trigger press, but it’s still running into a pretty heavy wall. Lighter than 1A, but still heavy enough to feel more like 1A than 2, and heavy enough to fit the 1A applications better than class 2 applications.
2) Heavy/Light: These triggers have a much lighter “wall,” such some inexperienced shooters who are not familiar with this type will often not even realize it’s a two stage, and simply slap these triggers like a single stage with long travel. These feel more like roller skating, then bouncing over the wall like a small seam in the road; just a slight blip in the otherwise smooth travel. Examples in this class are the Geissele triggers, or the old Bushmaster NM 2 stage. I personally consider these to be “precision 2 stage triggers,” as when shooting these triggers, most of the potential to influence the rifle with the trigger stroke has happened and recovered before a very light, crisp break. I don’t tend to hold these against the wall, certainly not very long at least - a smooth stroke against the heavy first stage as I slow the wobble, cut my breath as I find the wall, and break the shot, squeeze, breath, release... When shooting under stress or rapid fire, a shooter might not even notice the second stage because their dexterity is reduced and the sensation simply isn’t sufficient.
I personally prefer the latter group, heavy/light. I do more precision shooting than anything, and when I’m hunting under stressed time - like shooting hogs on the run - and I’ll make fast trigger pulls, I prefer having the heavier first stage to stabilize my pull instead of always feeling like I should have my finger taking slack out of my trigger any time I have my rifle shouldered to be ready for a quick break. I have a bunch of RRA 2 stage triggers because they are inexpensive, and I do manipulate the springs to become more balanced, adding weight to the front end and reducing the second stage, but I strongly prefer the second class to the first. Geissele and Bushmaster 2 stage triggers for me, please and thank you!