Imagine a ball bearing in a long, straight tube, so that it can only move left or right. Next, imagine a rubber string with black marks drawn at one inch intervals, so that when the string is stretched to twice its original length, the marks are now separated by two inches each. Now imagine that on that string are ants, able to move left or right, but that the string is being stretched too quickly for any of them to meet one another. These are the kinds if simple models physicists use to try to understand the universe in which we live.
The most common model I've heard is of a balloon with ants walking about its surface. As the balloon is blown up, the ants are pulled away from one another like the galaxies in our universe. Putting aside for a moment questions like what holds the ants to the balloon or what is filling it, we are still left with the problem that in extrapolating the two dimensional surface of the balloon to our three dimensional world there is no longer a convenient direction we can point to that we can call the 'inside' where the expansion comes from or the 'outside' into which it expands. For this, the model used is of a raisin cake rising in an oven. If we imagine all of the universe as filled with cake, there's no need for an inside, but our limited experience of perception then demands an 'outside' for the oven. Taken back to the balloon, we are misled by the fact that it has an outside as well, though the balloon itself has no edge. At this point, if we still don't understand the model, the physicist throws up his hands and we go off more confused than before.
But perhaps our problem is only one of scale. Let's look at the balloon more closely. At the microscopic level, the surface of a rubber balloon becomes more obviously three dimensional while the opposite side recedes into the distance. At these levels, we can see that it is actually a mass of long carbon molecules tangled so tightly that air can barely pass between. Looked at this closely, and from a point inside its skin, it is indistinguishable from a solid lump of rubber. Yet, when the balloon is blown up, a strange thing happens. It expands in the up/down and left/right directions, while it contracts in the in/out. The carbon molecules become more tightly tangled, yet the atoms they are made of don't expand. If we try to use this analogy for the universe, we have expansion in two dimensions but contraction in a third. The usual way around this is to imagine the balloon as an ideal sphere with only a two dimensional skin and add the third dimension upon extrapolation, like when going from a rubber band to a balloon.
However, we shouldn't throw out the thickness of the balloon so quickly. It turns out that in some theories of physics, the particles and forces of our world can be explained by having not only three spacial dimensions (plus one for time), but also six or seven 'extra' ones we cannot see. In at least one of these theories, six of these extra dimensions are of an unimaginably tiny, finite length and may be shrinking as the 'normal' three dimensions of the universe are expanding. If we fit these shrinking dimensions into our analogy of a 'thick skinned' balloon, it makes for a more natural model. We can now imagine the visible part of our world like the strands of carbon molecules in the rubber, being forever stretched out along their lengths while also being more tightly packed together in a direction the atoms cannot move in. Finally, the eleventh dimension that fits in with these theories, generally refered to as the Bulk, can be thought of as either the center of the balloon or the outside, depending on whether we imagine the balloon as expanding outward from its center or contracting inward toward a point at infinity.
If the idea of tiny, curled up dimensions is still difficult, try going back to the tube with the ball bearing. Now imagine that tube is turned around on itelf to form a hoola hoop. If that hoop, or torus, is again made of rubber and stretched out, the smaller radius will shrink while the larger expands. Next, imagine again ants walking around the outside skin of the hoop (and forget that the ball should be squeezed with the hoop's expansion). They can move in two dimensions, whereas the ball still can only move around it. Both directions in which the ants can move are finite, yet one is expanding and the other contracting, while the one direction the ball moves in always expands. If we take a large number of these hoops at odd angles to each other, yet all with the same center, and look at them from a distance, they begin to resemble the long carbon molecules in a rubber balloon. Every ball in this strange construction will still only move in one ever-increasing direction while every ant will still have one lengthening one and one shrinking one. This, extrapolated into eleven dimensions, is the model we are looking for. Matter in our universe moves only up/down, left/right, and forward/backward (as well as forward in time), while gravity can move along the extra dimensions as well, including the Bulk.