As mentioned, the fabric of space is a term used to create a better analogy for the way we perceive space to work. The rubber sheet analogy gets used a lot, especially when drawn with grid lines.
We talk about various massive objects 'resting' on this sheet and 'weighing it down' creating curvature about them, so that some of these previously parallel lines run closer to eachother.
It's possible to have an object so massive that it forces the lines around it to touch, creating a kind of isolated pocket-universe. Lines exist going in, but none out - we call this a Black Hole.
The analogy is also useful for describing it as the medium through which light moves. This is a little specious, however, as light's speed does not really depend on space's density, as you might call it.
The expansion of space is more than just everything within it moving apart from eachother. While it doesn't make a ruler grow (because the atomic forces binding it together vastly overpower expansion's attempts to make it do so) - it does allow for things to occur which would otherwise be considered to break Relativity - two objects actually receding from eachother at a velocity greater than that of the speed of light, due to the new space created in between them (though, 71 kilometers per second per megaparsec is not terribly fast).
I doubt science will offer much of an explanation before we get a Grand Unified Theorem, and that seems an unfortunate distance off.
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