The Copernican Principle refers to the idea that the Earth does not occupy a special place in the Solar System.
When Copernicus proposed that the Sun was the center of the Solar System (and by extension the Universe, as that term was understood during his time), he was essentially demoting Earth from a special place, the center of the Solar System, to an undistinguished place, the third planet from the Sun.
In recent times, the Copernican Principle has been extended to include the entire Universe. This extension of the Copernican Principle is called the Cosmological Principle, and it states that the Earth does not occupy a special or distinguished place in the Universe.
Neither of these principles are meant to imply that the Earth is not a special place, to earthlings.