The cosmological principle states the universe is homogeneous and isotropic when viewed on large enough scales. It is the ultimate extension of the Copernican Principle which asserts that the Earth is not in any special place in the universe. Mathematically this statement reduces to the Friedmann-Lemaître-Robertson-Walker metric solution to the Einstein field equations. In our expanding universe with scale factor a, as a function of time t, with the constant k representing the curvature of space (we have measured it and it is about zero), the angles θ and φ being the normal azimuthal and polar angles in spherical coordinates, and r being the radius, the metric solution to your universe is:
It is a beautiful thing that each observer is in a unique position to be at the center of their own observed universe because the expansion of the universe results in a coherent Hubble flow away from your point of reference in every direction. Thus one may entertain the notion that you are at the center of the universe. However, an external observer would also perceive that they are at the center of the universe. Thus, while observationally everyone is at the center of their own personal expanding universe, we logically conclude that this is merely an observational illusion of isotropic and homogeneous expansion. By carefully examining anisotropies in the cosmic microwave background or measuring the redshift of galaxies in different directions over time we can determine if the Copernican Principle is valid.