This guide will clearly explain how a semi auto AR15 trigger work and also clearly define the laws set by the ATF in the United States. The guide also includes AR15 trigger diagram and it's a comprehensive guide on how to operate it and how to be safe with it.
Animation is included to better explain all the moving parts.
How AR15 Trigger Works

The primary distinction between a semi-auto and full-auto trigger lies in the mechanism that determines how many rounds are fired with a single pull of the trigger. In semi-auto mode, one pull results in one shot, while in full-auto mode, the firearm will continue to fire as long as the trigger is held down.
AR15 Trigger Parts

Trigger: This is the "go" button. When you pull it, the rifle releases the hammer, which, if a round is chambered, will fire the weapon.
Hammer: This is a large, flat-faced piece of steel at the top of the trigger assembly. It rotates up and down, and its face strikes the firing pin inside the bolt carrier group, igniting the primer on a chambered round.
Sear: Located at the front of the trigger, the sear keeps the hammer cocked until the trigger is pulled. A cut-out on the bottom of the hammer engages the sear while at rest. Pulling the trigger angles the sear downward, releasing the hammer to strike the firing pin.
Disconnector: After firing a round, the bolt carrier group (BCG) is pushed back into the buffer tube by the gas system. As the BCG moves backward, it pushes the hammer back down into the trigger assembly. The sear usually holds the hammer down when cocked, but since the trigger was pulled to fire a round, the spring-loaded disconnector catches the hammer to prevent it from flying back up.
Hook: When the BCG forces the hammer down, a hook on the back of the hammer temporarily catches the disconnector. As you release the trigger, the sear moves back up to cock the hammer. The disconnector then slides off the hook, allowing the hammer to be held by the sear and cocked. The trigger resets, and the firearm is ready to fire again.
Check out this video showing how the trigger works
AR15 Trigger Spring
Why are mil spec triggers so heavy? About 6 to 10 lbs. While this is fine for military applications and safety, it's not great for those looking to make precision shots at long distances or rapid fire in competitions.
Part of the reasons is because the parts are not polished and the trigger spring isn't optimized. So you need a lighter trigger spring.
These are available to buy, and most aftermarket AR15 triggers have it included. These upgrades improve the trigger pull weight by eliminating any rough or jerky trigger feel.
AR15 Trigger Pin Size

Most AR15 on the market right now are all 0.154" diameter pin hole size. They are often referred as "small" pin hole size. Most AR15 trigger upgrades will label them as either "small" or "large". Most are small.
Large size pin hole 0.170" is mostly older semi auto Colt AR15 lower receivers back in the day.
AR15 Trigger Performance Terminology

Take-up: This is the loose feeling you get when you first pull a trigger. It's like squeezing the trigger without anything happening right away.
The wall: After any loose feeling, you'll reach a point where the trigger feels tight. This is "the wall." It's where the trigger starts to really work.
Creep: This is the trigger moving just before the gun fires. Some people don't like creep, but if it's smooth, it can help you shoot better. If the creep feels jerky, we call that "trigger stacking."
Stacking: This is when the trigger feels stuck and you have to push harder to make it move. It's not good because it makes the trigger unpredictable.
Pre-travel: This is everything that happens before the gun fires. It includes take-up, the wall, and creep.
Trigger break: This is the moment the gun fires.
Over-travel: This is how much the trigger moves after the gun fires. If there's a lot of over-travel, it takes longer for the trigger to be ready again.
Single Stage VS Two Stage Trigger

A single stage trigger is designed for rapid shooting, where the shooter feels the trigger wall instantly without any take-up, and the trigger breaks immediately. This design is ideal for competition and defensive shooting, offering a trigger pull weight typically between 3.5 to 5 lbs.
On the other hand, a two-stage trigger is tailored for precision shooting.
It features an initial take-up as the first stage, followed by a super light second stage trigger pull. This design ensures the lightest trigger pull without causing finger tremors, especially during long-range shots. The first stage acts almost like a preparatory phase, getting the shooter ready for the second stage.
While both designs have their merits, the choice boils down to personal preference and the specific shooting scenario. check out the comprehensive guide on single vs two stage trigger to learn more