The Copernican Principle proposes that the universe looks the same, whichever direction the observer looks no matter where that observer is placed. As such it is really more a statement of assumption, or origins science rather than observational or operational science based on strictly scientific data. It is often cited as being in opposition to the Anthropic principle. It is more or less synonymous with the Cosmological Principle which suggests that the universe is homogenous and isotropic on large scales. In other words matter is spread out essentially even, all across space in every direction with no boundary to space. It is often assumed by secular naturalists that the Copernican Principle is proven; however, nothing could be further from the truth.
Most seem unaware that the Copernican or Cosmological Principle is rather for the global structure of the universe breaking down more and more as it focuses on more and more local phenomena. So for instance a persons house and the local restaurant are obviously different. But as you pull out and bring into view the grander, global universe incorporating and comparing massive clusters of millions of galaxies in one portion of the universe to the other, it will look relatively similar. It is considered a property of the global universe.
- An Introduction to Modern Cosmology by Andrew Liddle. Page 19.