Mass and Energy can warp space-time around them, but that doesn't answer what space-time is, what is space?
closed as unclear what you're asking by Brandon Enright, Chris White, DarenW, centralcharge, akhmeteli Nov 26 '13 at 2:43
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David H is correct. If someone answered "Well, space is XYZZY" then you might, understandably, scratch your head and follow-up with "But... what is XYZZY".
Ultimately, as has been mentioned here numerous times, we get to the level of fundamental constituents of the world such as, for example, electric charge.
When we say that electric charge is a fundamental constituent of the world, we mean that electric charge cannot be explained in terms somehow "more" fundamental. If that weren't the case, electric charge would not be fundamental.
Similarly for spacetime or perhaps, the geometry of spacetime. Classically, at least, spacetime is fundamental so asking "what is spacetime" presumes that there spacetime isn't fundamental.
By the way, what is mass and what is energy?
String theory considers a 2-dimensional quantum field theory (in flat space) that contains, among other things, a set of 10 fields $\phi^\mu$, just like we consider an electric field as a group of 3 fields $E_x$, $E_y$, $E_z$.
Inside this 2-dimensional quantum field theory, there are a number of consistency conditions that must be satisfied in order for the theory to be well behaved quantum mechanically, just like any other quantum field theory. These conditions take the form of equations that the states of the theory must satisfy.
If we take the wacky point of view that the fields $\phi^\mu$ are the coordinates of a 2-dimensional surface in 10-dimensional space, then the states of the quantum field theory describe how the surface moves through 10-dimensional space (i.e., what is its metric), and some of the equations I mentioned previously turn out to be Einstein's equations coupled to Maxwell's equations.
So you could make this identification and say that spacetime is a state in some 2-dimensional quantum field theory. A lot of 2-dimensional quantum field theorists have made careers doing so :)