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The Copernican Principle is an assumption states, in simple terms, that we are not privileged observers in the Universe, which is to say that Earth is not at a special location within the Universe.
While such a belief may seem obvious and is typically the default today in science, it was not like this for a long, long time. Earth was first frequently conceived as the center of the Universe; however, later, the Earth was demoted to just a planet of the Sun, which was then the "true" center of the Universe. As we gained the ability to look out farther and farther beyond our own little bubble, we realized that even the Sun is not particularly special, and then saw that even our galaxy is not particularly special within our great universe.
The Copernican Principle is one of the foundations for modern science and especially for relativity and cosmology. It cannot be proved, but everything we have observed about the universe at large seems to support this assumption. In order for us to understand the Universe, we must first accept that we are not special.