general relativity - What do we mean by space is expanding?

Indeed space is not a physical entity (as far as we know). Saying space expands is another way to say that galaxies recede away from each other at a rate proportional to their distance.

The "expanding space" picture is unfortunately a source of endless confusion and misconceptions, as can be seen on the page of this very question: mpv mentioned that "The real expansion of space would manifest itself in the following way: you have 2 rockets in empty space, stationary with respect to each other. None of them starts its engines, but yet, they start moving away from each other."

This is plain wrong, the "expansion of space" is not some magical force that pulls objects away from each other. If you mean empty space as in no dark energy, no dark matter and no visible matter then the two rockets would move towards each other due to their mutual gravitational attraction (if you neglect their mass then they would not move at all). In the general case what will dictate the motion of the rockets is their gravitational attraction, the matter nearby (visible and dark) and dark energy (whatever that might be), the combination of which might pull them closer or further away from each other. The expansion of space is not an additional force. Galaxies don't keep moving away from each other because some undetected substance is created between them, but because they have an initial velocity which they acquired at the time of the big bang: without anything to stop them they keep moving away.

Joan.bdm said: "As I said in a large scale all objects recede from us, if it wasn't for the space expansion it would mean we are at the center of the universe."

The second part of the above sentence is wrong as well. As long as all galaxies recede from one point at a rate proportional to their distance, it follows that from ANY point all galaxies will be seen to recede at a rate proportional to their distance. This is easily seen with a little drawing (each * corresponds to a galaxy):

Before

After

If all galaxies are seen to recede at a rate proportional to their distance from the point of view of the galaxy at the center, then from any galaxy all other galaxies will be also seen to recede at a rate proportional to their distance.

I don't think we have any satisfying explanation as to why galaxies move away from each other at a rate proportional to their distance in the first place. The "expansion of space" is not an explanation, it is an analogy. A related and interesting read: Expanding Space: the Root of all Evil?