On the largest cosmic scales, the Universe is both homogeneous and isotropic. Homogeneity means that there is no preferred location in the Universe. That is, no matter where you are in the Universe, if you look at the Universe, it will look the same. Isotropy means that there is no preferred direction in the Universe.
Isotropy means that there is no preferred direction in the Universe. That is, from your current location, no matter which direction you look, the Universe will look the same. Diagrams like the one above of the distribution of galaxies in the Universe seem to imply that the Universe isn't homogeneous and isotropic.