What does the cosmological principle state about the universe?
The cosmological principle states that the Universe is homogeneous and isotropic when viewed on a large scale.
The cosmological principle implies that the matter distribution in our Universe is homogeneous and isotropic on a large scale.
This comes from the fact that Although the universe is inhomogeneous at smaller scales, it is statistically homogeneous on scales larger than 250 million light years. The cosmic microwave background is isotropic, that is to say that its intensity is about the same whichever direction we look at. 
The cosmological principle also implies that our Universe is non-static and flat.