To paraphrase Lawrence Krauss:
"In quantum mechanics, nothing is always something."
Space exists. There is no perception about it, really. Whether as matter or energy waiting to be converted into matter (or vice versa) it is "something" at all times, even if we do not fully understand the constituent parts.
The whole dark matter / dark energy (and people with more info on these subjects can correct anything I may mess up here) hypothesis are representative of the unknown "stuff" of space. The fact that the expected measurements necessary for a certain "structure" to the universe (open, closed, or flat) match experimental values so far indicates that we have a fairly good idea that a) the "stuff" exists and b) the ratio of the "stuff" out there.
Basically, while we don't understand, specifically, the exact nature of the "stuff" of space - we can measure it and base predictions off of it that end up being extraordinarily accurate - therefore we can reasonably assume that (until better evidence comes along) the universe is not some abstract philosophical construct, but rather a medium through which matter and energy interact via the fundamental forces.
Back to the first thing I said, and the others can explain this way better than I can, but matter and energy freely and spontaneously convert back and forth between each other. The "nothingness" of space is actually a massive body because of this principle. The total overall mass of the "stuff" is slightly positive (which balances out the slightly negative total energy of gravity [fact check here maybe?]) because of a infinitesimally small tendency to exist as mass longer than energy. (again, fact check by the quantum experts here).
Dunno if that clarified anything? Or if it just made you more confused
tl;dr of the "stuff" existing is that if we can make experimentally testable predictions based on the expected presence of something, and the predictions are accurate and true, that something exists.