The following information can be found here https://www.warhistoryonline.com/guns/how-a-bullet-works.html

To begin answering this, it is important to know that using the term “bullet” to refer to a round of ammunition is, in fact, wrong. What many refer to as a bullet is actually a cartridge. A bullet is only a small component of a cartridge, not the whole cartridge itself.

The Case

This is a type of container which holds all other components of the cartridge. At the base of the case, you’d find the primer; in the middle, you’d find the propellant (gunpowder); and at the top, you’d find the bullet. The case is the part you see being ejected from the gun in automatic and semi-automatic weapons each time you pull the trigger (in revolver and single shot weapons, the case remains within the chamber).

The Primer

The primer is located at the base of the case. This is basically where the firing chain is initiated.  Separating the primer and the propellant is a small gap called the “flash hole” through which ignition sparks travel to set off the propellant once the trigger gets pulled.

The primer receives the impact of the gun’s firing pin.

The Propellant

The propellant is simply a technical term which refers to what is commonly known as gunpowder.

The gunpowder is, characteristically, a rapidly burning substance that creates rapidly expanding gases which develop pressure within the walls of the cartridge. These very high-pressure gases seek an outlet through the path with the least resistance, which would be at the other end of the cartridge where the bullet resides.

The loud bang you hear when a gun is fired is due to the break out of the pressured gases through the barrel.

The Bullet

The bullet is referred to as the “projectile” by some people. It sits in the other end of the cartridge, and all the actions of every other component are geared towards pushing this particular item out of the cartridge and out of the gun with enough speed to hit its target down range.

How Does this Work?

You pull the trigger and a loud bang follows. Seems pretty fast and straightforward. However, within that split-second of firing, there are several processes going on within the gun, all of which occur extremely rapidly.

When the trigger gets pulled and the primer receives the strike of the firing pin, a small spark emerges igniting the propellant.

This propellant burns rapidly, releasing gases at high pressure. By virtue of these gases, enormous pressure is exerted inside the gun.

Newton’s third law of motion states that if an object exerts an amount of force on another object, the second object retaliates by exerting an equal force in the direction of the first object’s force. This is why you feel the gun leaping backward when it fires a bullet.

So, when the propellant exerts pressure on the gun, the gun exerts an equal and opposite force on the case containing the propellant and other components including the bullet.

As the gases seek a way out, they are channeled through towards the bullet which offers a path of relatively low resistance for a breakout. The gases push the bullet out of the case and through the gun’s barrel as they escape, all accompanied by that loud bang.

Guns come with spiraling grooves within the barrel called rifling. These grooves make the emerging bullets spin as they travel through the air. Spinning makes the bullet break through resistance much more effectively, continuing in a straight path towards its target.

Refer to the video below for an in depth look into how bullets work.