A more scientific statement is that the universe is both isotropic and homogeneous. Isotropic means that the universe looks the same in every direction that we (on Earth) look. Homogeneous means that the universe looks the same to every observer.
Isotropy. An isotropic universe looks the same in all directions. At the scales we are used to dealing with, isotropy does not appear to be true: the Sun, planets, Milky Way, etc. are only visible when looking in the right direction (the same is true for clusters of galaxies). However, these distances are small compared to the scales we use in cosmology. Counts of distant galaxies and radio-sources appear to provide evidence that the universe is isotropic.
Homogeneous. A homogeneous universe is one that looks the same to all observers. Obviously we cannot check that the universe is homogeneous - it is difficult for us to travel to the nearest planets - let alone the most distant galaxies. Instead we must try to infer whether the universe is homogeneous. A rough argument is as follows:
The cosmological principle is a working hypothesis of cosmology. With the CP, our knowledge of our local surroundings can be extrapolated across the whole universe. If the cosmological princple is false then we cannot infer anything about the un-observable regions of the universe.