I liked what Brainstorm said about Goethe's theory of colors. People have a knack for taking things and making them way too complicated. But then again, at the same time, Einstein and Newton only made advancements through thought experiments. The only reason we have relativity is because Einstein was so inquisitive and spent so much time thinking of abstract ideas.
The only way to get anywhere is with this sort of abstract questioning, but in order to make sure we're going in the right direction, we need to make sure our theories match current experimental evidence, which is where Goethe failed with this theory of colors. Speaking of which, our "theories" are actually just hypothesis until we actually experiment with them.
Anyways, Fredrik stole the words from my mouth. I was about to post about how science can only really confirm hypothesis through experimentation, which is, by definition, the scientific process. Forming our hypothesis is arguably bordering the realm of philisophy. We think of the universe, try to understand it in ways that make sense to us. We try to form a picture, and our picture says X should behave so. When X doesn't behave so, we're wrong, when it does, we test again and again until we're sure it doesn't. After all, it's only when we're wrong that progress can be made ;-) . How boring would it be if everything you thought of was right? (Though, it would arguably be quiet awesome. I guess it's more correct to say, how much fun would it be if other people were always right?)
Alright, almost forgot. Speaking of "making sure X behaves so", franklinhu, if the effects of relativity come from velocity increasing the number of reactions that must take place, then the Lorentz factor would be linear, since doubling speed doubles the units of distance you travel per unit of time. If we describe each particle pair as a unit of distance, than doubling the speed would double the number of required reactions. Tripling it would triple it, etc.
However, the Lorentz factor follows the equation of (since my keyboard doesn't have the actual "Lorentz" symbol :P )
L = c / sqrt ( c^2 - v^2 )
Which is certainly not linear. Time to go back to the drawing boards with that idea. No shame, when it comes to light bulb filaments, Edison was wrong several thousand times and he was only right once. Not to say his invention didn't make any difference :-)
EDIT: To expound on this a little more, it's not "nobody knows, nobody cares, nobody can know", it's more along the lines of a challange: "Come up with something that WORKS!", that is, when put to the text of experimentation.
Hmm... It seems just about everybody has their own little theory about the universe. There's nothing really wrong with that, it's just it can't be taken seriously unless it's proved itself through experimentation. Make the theory, write it out in MATH, so there's TANGIBLE implications. If reality follows the pattern, keep going, you may be onto something. If reality doesn't follow the math, don't worry, that just means your one of the six billion others who aren't revolutionizing science ;-)
If you want to do more in this area, then take courses in physics and get used to describing EVERYTHING with math. Once you've done that, then I'd say join the club. But I can't technically say that since I'm not "in the club"... yet :p .
Back to the original question, a little apology to the OP since we've gone so OT,
from my understanding space is the distance in-between objects. In the strict mathematical sense, it's a decay in the amount of force objects exert on each other. If gravity is a force, then this would hold true.
However, if gravity is a curve, which definitely seems to be the case, then space is really more of a 4 dimensional fabric, where the fourth dimension is time, as intrinsic to the fabric as the spatial dimensions are. Which, lol, didn't really answer the original question. So to answer that, then I think I'd say space is the gravitational potential an object has, along with it's relation of how strong other objects' forces exert on it. Essentially the same answer as the "strict mathematical sense", except with the gravitational potential bit added on.