I am sure physicists have addressed this question many times before, but I never heard it addressed, so I offer my own explanation which may be totally off - but it sounds correct.
The question is "what is at the end of the universe?". Of course, to ask such a question one must assume to begin with that the universe is finite in size. All the current knowledge that science has learned about the universe points to the conclusion that it is finite in size and there are even estimates to just how large it is. Furthermore, the universe is expanding, it is getting larger and larger, but at every moment it is finitely large.
There is an obvious question that every person must ask, "if the universe is finite in size, then what lies beyond it?", or to put it another way, "what can lie beyond empty space?". Is there some sort of magic barrier that if we are to reach the edge of the universe we will crash into? Because saying that the universe is finite in size sounds as if there is an edge that we cannot walk over for if we were able to walk over then we will still be in a universe.
I believe that the explanation is very simple. This question of "what is at the end of the universe", or "what is beyond the universe", or "where is the edge of the universe?" sounds so surprisingly similar to the question of "what is at the end of the world?". This question was once asked, 500 years ago. People used to insist, 500 years ago, that the world was flat as it is finite and so that if we reach its edge we will fall off the world.
Intuitively such a primitive answer makes sense. But we know what the answer to that question is. The world is a sphere, there is no edge to it, when we move on the world we are simply moving along an arc of a circle. If we keep on moving in the same direction long enough, we will not fall off, but return to the same place where we were standing!
I believe the same answer can be generalized to the universe. The world that we know of is the surface of a two-sphere (two dimensional sphere) living in (embedded) a three-dimensional space. We can so too say that the universe is a surface of a three-sphere (three dimensional sphere) embedded in higher dimensional space.
The consequences of such a way of looking at the world immediately leads to an interesting conclusion. It means that if we are to move straight (relative to ourselves, but really curved with relative to higher dimensional space) long enough we will eventually return to were we started in the universe! However, this cannot happen. For the reason that the universe is expanding, and as we travel, the universe expands as well, thereby increasing our total travel and making it impossible to return back again.
There is a problem however. The version of geometry used in cosmology is hyperbolic geometry, and I am thinking of the universe in terms of elliptical geometry (as I am thinking of us living on a surface of a higher dimensional sphere). This is inconsistent with cosmology, so I am not sure how to resolve this contradiction.