The galaxies are not uniformly distributed in space. Many galaxies are part of larger gravitationally bound systems; these galaxy clusters can contain hundreds of galaxies. The galaxies within a galaxy cluster orbit center of the cluster, but the orientations of the orbits are random, so that the cluster as a whole has no definitive axis of rotation. This randomness allows galaxies to pass near one another, causing them to disrupt one another through their mutual gravitational attraction. A consequence of this is that larger percentage of the galaxies in a cluster are elliptical galaxies than in regions of gravitationally unbound galaxies; the spiral galaxies are destroyed through repeated encounters with other galaxies in a cluster.
Besides the gravitationally-bound clusters of galaxies, we see numerous galaxies lying in great sheets that surround regions with relatively few galaxies. This inhomogeneous galaxy distribution gives the universe a mottled appearance, as if the universe were built of empty bubbles enclosed by walls of galaxies. These bubbles, while quite large in comparison to the size of a galaxy, are very small compared to the size of the observable universe.
The most striking feature we see when we look at the galaxies is their motion: the galaxies on average are moving away from us, with the speed of recession proportional to distance when the speed is much less than the speed of light. This striking feature holds regardless of the direction we look, so this recession gives the illusion that we are sitting at the center of an expanding universe. In fact, an observer on one of those very distant galaxies would see precisely the same effect: all galaxies would be receding isotropically away from him, with the rate of recession proportional to the galaxy's distance from him.
One unavoidable conclusion of an expanding universe is that in our past the universe had a much higher density; if we extrapolate far enough back in time, we find a time of infinite density; we define this time as the beginning of the universe. This is an extrapolation based on our current understanding of physics; we do not understand the physics in play at the high densities encountered in the early history of the universe. The precise age of the universe is uncertain, but it is most likely between 9 and 16 billion years.
If we look far enough out, we see galaxies moving away from us at nearly the speed of light. This extreme motion at extreme distance changes the universe's appearance to us. The light from the most distant galaxies is Doppler shifted into the infrared, which is invisible to our eyes—while infrared telescopes exist, they are much more limited in their capabilities than optical telescopes. The most distant galaxies we see are also younger than our own Galaxy and the nearby galaxies, in part because light takes a finite time to travel a given distance, but more because time passes more slowly for objects moving away from us at close to the speed of light.
So what, precisely, do we see? As we look out, we see galaxies with very active nuclei—galaxies with central black holes that are radiating tremendous power as they consume gas and stars. We also see galaxies giving birth to massive numbers of stars. The most distant galaxies contain much less iron, nickel, and other products of thermonuclear fusion that our own Galaxy. Looking farther out, the galaxies eventually disappear from sight as their light is Doppler-shifted into the infrared. The universe beyond this distance is invisible to us until our instruments reach a region so dense that light cannot freely propagate. This region is so young that it contains only hydrogen, helium, and slight traces of other light elements; stars and galaxies are completely absent. For this region of the universe, no more than 150,000 years have passed since the universe's beginning. This region defines the physical edge of the observable universe. It is a photosphere, much like the Sun's photosphere, radiating energy towards us, acting as a surface that completely surrounds us. Someone at this photosphere would measure a temperature similar to the temperature at the Sun's surface, but to us, who see this region receding at close to the speed of light, the Doppler-shifted light emitted by this photosphere is the light of a cold body, a body of only 2.7° Kelvin, appearing to us as microwave radiation.
The amount of matter in our visible universe is uncertain; it may be enough to decelerate the current expansion, or it may be too small for its gravitational field to alter the expansion. What we can say is that mass of the universe out to where we cease seeing galaxies is less than 1023 times the mass of the Sun, or less than 100 billion times the mass of our own Milky Way Galaxy. Our Galaxy is an insignificant fraction of the observable universe.
When the ancient astronomers look into the sky, they saw themselves at the center of a celestial sphere, with all of the planets and the Sun orbiting Earth. Now with our current instruments we find ourselves with a similar view of the universe: looking out beyond our Galaxy, we see ourselves at the center of a sphere, unable to see beyond the surface of that sphere. But the similarity is only in appearance. Our theory, which explains the observations very well, is that all places in the universe experience the same evolution, so the region providing the edge to our universe, the gas of this distant photosphere, will in its own time evolve into stars and galaxies, and if intelligent life arises on a planet in one of these galaxies, those beings would see the same universe we now see—an expanding universe of galaxies bounded by a surface of gas.