Okay kiddo, so you know how when you look up at the sky, the sun and the stars all seem to be moving around the Earth? Well, a long time ago, people believed that the Earth was at the center of the universe and everything else was moving around us. This idea is called the geocentric model.
But a guy named Copernicus came along and said, "Hey, what if it's actually the opposite? What if the sun is at the center and the Earth (and all the other planets) are moving around it?" This idea is called the heliocentric model.
The Copernican principle is the idea that the laws of physics and nature are the same everywhere in the universe. So, no matter where you are in space, the rules that govern how things work are always the same.
Basically, Copernicus showed us that we're not the center of the universe and that the same things that work here on Earth also work everywhere else. It's kind of like saying that all the toys in your toy box work the same way, whether they're on the bottom of the box or the top. It doesn't matter where they are, the rules are the same.