Inside, you'll find a tungsten filament suspended between two spires. Electricity travels up one spire, across the filament, and down the other spire. In the process, the filament heats up, glows, and emits light.
Incandescents work because tungsten is an incredibly durable chemical element with a melting point that's about as high as it gets. It can handle the heat, but it doesn't make for a very efficient light bulb, because all of that heat is really just wasted energy.
As you can see, there's still a filament here, but it's encased in a little chamber. That chamber also contains halogen gases like bromine and iodine -- their job is to essentially recycle some of the evaporated tungsten back onto the filament after it burns off so that it can be used again. This extends the life of the bulb, and also helps it put out more light using less energy.
For starters, you get a cool GIF like this one. You'll also see a little puff of gasses escaping -- those are the bulb's namesake fluorescent gasses. They include neon, argon, and mercury vapor, which gives off light when you pass electricity through it. Mercury is pretty toxic, so if you break one, you'll want to be pretty careful about how you clean it up.
It's all in the name. "LED" stands for "light-emitting diode," and inside, you'll find a bunch of them. Each one is a tiny junction with two nodes. When electricity passes through, it jumps from one node to the other and gives off light in a process called electroluminescence.
LEDs also promise to last years or even decades, which makes it more important than ever to buy the right bulbs for your home. That's why we test and review the latest light bulbs (and why, on occasion, we smash them, too).