The Fabric of Space-time? I am not an academic in anyway, just someone interested in the story that is our universe. So my apologies if this isn't a well thought out inquiry.  
I've been struggling with a concept for some time (which is probably rudimentary) that I can't even frame into the right words to know where to begin a Google search, so thought I'd try this platform. 
I'm trying to wrap my mind around the fabric of space. I can understand the effect of a mass like our Sun and its gravitational influence on the fabric of space, and how the planets fall into indents orbiting that mass. But my questions is, are all the masses in the universe on top of that "fabric"? Essentially, I'm asking if the fabric of space is all encompassing in the universe, is it at all points North, East, South, West, above, below, in between, or just a horizontal plain that all masses reside upon? I know that space-time twists in relation to a mass, is space-time manipulated the same way above the Earth and Sun as it is below? 
Not sure if I'm framing this question correctly, but any insight you can provide would be beneficial.      
 A: The FABRIC OF SPACETIME
What does the question and the concept mean?
It's not a scientific question, there is no such term as fabric in physics. Rather, it is a generic conceptual question meaning a few things:
1) QUANTUM GRAVITY: What is its microscopic structure?: what is spacetime made of? What is it's fine structure, as if you looked from close up, as a surface, a fabric? What is it that is interwoven that makes it be what it is? 
2) GRAVITATION: What of it's dynamics?: How does it behave and why? What are its mysteries and strange ways by which we see objects moving and changing?
2) COSMOLOGY: What is it's large-scale structure?: How does it look in the large, from a distance? What makes it be anything more than an empty canvas on which matter and energy travel and interact? 
The term fabric tends to be inspired by the first question -- what does it look like when you look close up?. But if you pull away from looking at the fine fabric, you see the astrophysical regime of stars, galaxies and clusters, and as you see from further away you see the universe in its larger scales. You may also wonder if there are more universes. All of these have to play into each other, so they need to be related. At this point in our understanding of the physics of spacetime, we know better how to try to answer questions 2 and 3. Those can be for the most part (but not fully) explained by General Relativity (GR) which explains Gravitation, and the more or less known physics of classical mechanics, electromagnetism and thermodynamics, along with the modern physics of quantum mechanics (QM), quantum field theory (QFT), and the Standard Model (SM) of particle physics, which together explain atoms, electrons, protons, neutrons, photons and other elementary particles.
The first question, about spacetime in the small is harder, we have no real data about gravity at distances smaller than maybe about 1/10 of a mm, where Newtonian gravitation still seems to hold. And have not been able to explore the even smaller distances that require energies much larger (some think maybe not that much more, if there are extra dimensions of certain sizes) than what we can produce in the LHC, our most powerful particle accelerator.     
So, really, it's a big question. The easiest way to get a grip is to first simply bring in what we do know. That's part of the answer to questions 2 and 3. It gets more speculative, and strange, for question 1. 
A good reference for spacetime is in the wiki link here
As Heather described in her answer, spacetime is like that 2 dimensional fabric we see bent or deformed in many popular descriptions, like the figure below, except it is 4 dimensional -- well, she makes clear that's very different. That's why she says to try to wipe that figure from your mind, it's the 4 dimensions that makes it real and true. The sheet doesn't bend down below the earth in reality -- the earth resides in that 4 dimensional spacetime, and actually moves through it, both in the space dimensions, and evolves to the future as time goes on. In 4D we see its time history of it, its so called worldline. We can't draw on 4D, but in we can ignore one of the spatial dimensions, and draw a spacetime diagram in 3D, as the next figure shows.
 

The earth does in fact deform the 4 dimensional spacetime. The next figure helps a little visualize the paths of light rays and see their deflection due to gravitation.
 
But as Heather said, it is really 4D, and it's hard to visualize. And as Countto10 says, it can be pretty complicated. 
So WHAT IS GRAVITATION, as described by GENERAL RELATIVITY?
It's the 4D spacetime, along with equations that relate the geometry of spacetime to the distribution of matter-energy in that spacetime. It's an equation like,

that determines (partially, some initial or boundary conditions or symmetries which define the context are needed to get a unique solution) the geometry of spacetime. From it one can solve for the metric, $g_{\mu\nu}$, which completely defines the geometry (the R terms on the left hand side are functions of the metric and its derivatives up to second order). For this one obtains all the solutions like Black Holes, gravitational waves, and the orbits of the planets and stars.  
But, WHAT OF THE MORE EXCITING AND OUTLANDISH PICTURES LIKE THE UNIVERSE EXPANDING AND WORMHOLES CONNECTING DIFFERENT PARTS OF SPACETIME? 
Well, yes, for that we have to do more work. WE have to solve the equations that describe the evolution of the universe (with the help also of the equations for the matter-energy on the right hand side). And it is done, and results in the Lambda-CDM concordance model, with the universe expanding and as we now know accelerating, and the Cosmic Microwave Background coming from when radiation was let loose 380,000 years after the Big Bang. See for that the chronology of the universe at the wiki article here
As for wormholes, they are hypothetical structures of spacetime that would connect one region of spacetime with another very far away. They've not been seen, are theoretically unlikely but possible if we had exotic material (negative mass , other possibilities), also not seen. See wormhole in the wiki article at https://en.m.wikipedia.org/wiki/Wormhole 
And WHAT OF THE QUANTUM PICTURE OF THE FABRIC IN THE SMALL, THE MICROSCOPIC VIEW?
Well, it's more speculative since we still don't have an accepted theory of gravity at very small distances and very high energies. Two most cited theories are string theory and quantum loop theory. In one way or another it leads to a highly dynamic high energy submicroscopic spacetime, bubbling and changing, and somehow causing what we see as spacetime now to emerge. See . 
Another factor that comes in and is still possibly in play is multiple dimensions, with perhaps 6 really compacted dimensions at every 4D spacetime point, such as the Calibi Yau manifold . 
There's other variations with large higher dimensional spacetime membranes. See String Cosmology here
WHAT'S THE FABRIC OF SPACETIME?
It's some unknown combination of those and a few others. We're still trying to figure it out. 
Figure and Link References: 
  https://en.wikipedia.org/wiki/Spacetime
https://i.stack.imgur.com/2fthm.png
https://i.stack.imgur.com/GmLd2.png
https://i.stack.imgur.com/pYYeY.gif
https://i.stack.imgur.com/9MjYs.png
https://en.wikipedia.org/wiki/Chronology_of_the_universe
https://i.stack.imgur.com/lD8Sk.png
https://i.stack.imgur.com/HNvwF.png
https://en.wikipedia.org/wiki/String_cosmology
A: To better picture general relativity you need to first discard the common concept called "the force" of gravity. GR is not based on an attractive force between Earth and Sun.
Now if you want to explain why we are orbiting around Sun you bring the theory of general relativity. It says that spacetime is curved around Sun. So there is no other way around for Earth to move near to Sun but to orbit even when it is free and there is no force upon it. This is because the space is curved. Also if you are much closer to Sun the orbit pattern is not fixed in time. It changes and evolves because time is also curved. And people closer to Sun do not agree with you sitting on Earth about passing of time with respect to a series of events because they have their own different clock. Yet you and they would agree if measure the same event in terms of spacetime.
Now imagine you are far away from Sun. Spacetime is not that much curved. Earth would have moved in a straight line forever because spacetime is flat.
Also imagine that you are interested in the movement of Earth over very short distances in spacetime even close to Sun. Again spacetime is not that much curved. You can approximate with a straight fixed line in spacetime.
General Relativity should not be formidable to learn even with involved levels of mathematics. It is about having a single formula relating dynamics of mass-energy to geometry of spacetime. This formula remains spectacularly valid even if you play around with countless combinations or variations of spacetime coordinates. Some of the combinations of coordinates are, however, much simpler to draw and to make sense of them in four dimensions.
When applied to the whole universe it gives you clear insights about the past, the epochs that have passed, and of course the future plausible evolutions of the universe. In particular it helps you picture if the universe will continue expanding, or contracting, or oscillating indefinitely, or there might be other universes nearby on gigantic scales of spacetime.
A: I have always had a huge problem with people describing gravity in these terms.
Even if it doesn't take 4D into consideration it also uses gravity to explain gravity. Bassicaly it says that bigger the mass, the bigger depth in the fabric it falls into. But for other objects to be accelerated towards those masses it requires a gravity to be pulling them downwards. So this description is one of the worst  I've ever seen.
Never explain a thing with using a thing you're explaining. It's like saying a car is red because a collor red looks red.
A: The rubber sheet analogy, and all pictures that go with it have mislead many people (including me) and so now I must request that you completely and utterly banish that thought from  your head. No sheet. 
Instead, imagine it as a series of grids, like sheets of graph paper, spaced such that they are parallel to each other, going in each direction for infinity. And now, imagine another set, perpendicular to the first. If this is a bit hard to imagine (which it is, this is very abstract) you might try imagining the Cartesian coordinate system in 3 dimensions and putting in the gridlines. Now, we put in objects. Before we continue, remember, this extends infinitely in ALL directions - up, down, left, right, forward, backward (or whatever passes for these directions). 
Set an object, let's say a planet like Earth, into these grids. Make the grids "come toward" the Earth, so that the Earth is sort of "sucking in" the grid around it, and pulling other nearby objects enmeshed in the grid towards it. This is a three dimensional universe. But there are four dimensions...there is also time. We cannot picture four dimensions, except mathematically, as Countto10 said, so merely keep this in mind instead of trying to add this to your mental image. 
So, to more explicitly answer your question, spacetime is all around - there is nothing outside of spacetime, and there is merely the objects within it. These bend and twist spacetime, therefore affecting other objects. 
Hope this helps; I'd be glad to clarify further if necessary.
A: I read through the possible duplicates, but I could not see an answer that I could be sure you would like.
When you speak of things like "fabric", obviously it is a metaphor for spacetime, but unfortunately  it's a 3 D metaphor, as we can't think in 4 D, except when we calculate math, if that makes sense to you.

But my questions is, are all the masses in the universe on top of that "fabric"? Essentially, I'm asking if the fabric of space is all encompassing in the universe, is it at all points North, East, South, West, above, below, in between, or just a horizontal plain that all masses reside upon? I know that space-time twists in relation to a mass, is space-time manipulated the same way above the Earth and Sun as it is below?

I would ask you to think about what you have written, it is all phrased in 3 D terms. I would also ask you to pretend you have never seen any "artistic rendition" of the universe, as they are all incorrect or simplified to the point of complete distortion.
Instead, follow through on your question to its logical conclusion. What do you imagine the universe is "like" on a large scale, or where does the "fabric" end?  Any image you have of curved spaced,  a giant sphere or a toroidal shape is based on the only experience we all have, that of three dimensional space. So that's not going to get you very far, as you are going to ask what's "outside" this shape.
My suggestion to you is to think of space as a distance based idea, but only for short distances, relatively short that is, from Earth to Betelgeuse the space as distance idea will be fine. 
On a universal scale, you might consider spacetime not as a "thing/fabric", but as a way of describing how the objects in the universe relate to each, both in space and time. This idea is very abstract I  admit, but tell me any part of modern physics that is not? 
150 years ago, energy was not viewed in discrete terms, but now we know it is, although we don't have an idea why (at least I personally don't).
My point is, on the small scale, we had to redefine our word energy, and on the large scale, we may need to redefine our concept of spacetime from distance terms to relationship terms. 
A: The spacetime of general relativity is highly dynamic. Static representations are very misleading. Static representations include the rubber sheet metaphor, which is static because the rubber sheet is just there, implying an all-encompassing Euclidian background that does not exist; they also include the block universe where the whole of spacetime is seen somewhat from outside, which is impossible since Einstein's equations are only local.
We can only experience spacetime from inside, and only locally. Thus, there is no really any fabric in the sense of something that all observer would agree is objectively present everywhere. What we have are relations: how what an observer measures can compare to what another observer measures, knowing how the two observers move relatively one to the other. What these relations show is that there is no Newtonian space acting as an empty container for things to live in, and that there is no global notion of simultaneity either, so there is not an universal time valid for all observers. 
It can even be said that in the absence of matter, spacetime is not even defined: this is (vastly simplified) the hole argument; there is no container where there is no contents! See also Mach's principle.
If we dig further, we can see that what spacetime gives us is only a set of symmetries, allowing us to "transport" physical laws from a frame of reference to another. And strikingly, Wigner's classification of fundamental particles links them to the Poincaré group of the symmetries of spacetime, so this is another venue, after the hole argument, pointing out that in a certain sense the contents of spacetime (in that case, particles) is spacetime.
So, maybe we are the fabric of spacetime.
