First of all, when referring to bullets, most people actually mean cartridge. The cartridge is the entire object that is placed into the magazine or directly into the gun. Many different types of cartridges have been used throughout history, but today we will be discussing the modern, centerfire cartridge. This is what will be used in most semiautomatic handguns.
The first part that we want to identify is the primer. Think of it as a starter for a car. It is located at the rear end of the cartridge and is engaged by the hammer or striker, causing a small explosion of the priming compound upon impact. This explosion begins a chain reaction that will eventually make the gun go "bang".
The next component is the propellant or gunpowder. It is a substance, ignited by the primer component, that forces the bullet to be pushed out of the gun. It was first invented in China sometime in the 9th century AD. It has changed some over the years, but its intended purpose has remained the same.
We all know that the main objective of a gun is to fire the projectile or bullet. This is the metal object that leaves the barrel of the gun and hits the target. There are many different compositions of metal that bullets can be made. The most common types for handguns are full metal jacket (FMJ) and jacketed hollow point (JHP). FMJ bullets are composed of a core, usually lead or steel, encased in a coating of a harder metal, usually copper. The case can cover the entire bullet or just the sides & nose. In JHP bullets, the objective is to maximize the energy exerted on a target. They are designed to spread apart on impact, therefore limiting penetration and remaining in the target.
The rim of the cartridge is where the primer is housed and is designed to give the extractor a place to grab onto in order to pull the spent casing out of the firearm.
Finally we have the bullet case. This is the metal that holds all the other components together. Once the cartridge is fired, the case will be ejected from the firearm in order to make room for the next cartridge to be inserted.