Shaders are computer programs that run for every pixel in your screen. If you know the math, you can draw anything!
Think of it like this: your computer screen is full of colors and shapes. Those shapes are made of tiny lights arranged in a roughly grid-like pattern. Now, what if you could create a recipe that tells the computer what color a single light should be?
The computer runs this program for the millions of pixels of your screen, and it does this upwards of 60 times per second. The result is called a shader, and they are the technology responsible for most of the graphical effects in modern games, among many other things.
Visit my ShaderToy profile to take a peek.