I think it means that it's expanding and traveling in the opposite direction of us. If we start at the same spot, then both travel in opposite directions at 1 mile/hour, at the end of an hour we will be 2 miles away from each other.
There is not really a center, galaxies are more like raisins in a rising bread. They all move away from each other with the same relative speeds. At least... Any physicists here to tell me whether or not space-time density get less closer to the edge? I mean... Is there an Edge?
There is no edge. It defies the normal way of thinking but every point in the universe is also the center of the universe. The Big Bang happened at every point and space-time is expanding at every point.
Well, not really. The distance we can see out is measured in time and we can very nearly see the Big Bang. We can observe the Universe's Recombination event and it is in every direction we look as the Cosmic Microwave Background. This happened everywhere in existence.
If there is an edge to the Universe it is in the fourth dimension when the Universe was a singularity.