This seems to be the prevailing theory of the shape of the universe. My familiarity with the theory is shaky at best, but basically it states that the universe is not infinite in size, however, you can travel an infinite distance without "falling off" of the universe. How is this possible?

Imagine the Earth. More or less spherical in shape. You can travel across the Earth in what you perceive to be a straight line, although it is slightly curved, without falling off. Yet we know perfectly well that the Earth is not infinite. This is possible because the line, which is straight on axes x and y, (we're assuming a Z-Up Orientation here for the sake of convenience) is slightly curved on axis z.

Take this idea and add a 4th dimension. Now you can travel in a subjectively straight line on axes x, y, and z, and you'll still returned to the same place because of the curvature of the 4th axis. The shape I have described is a hypersphere. I've also heard theories that the universe is a hypertorus, which I can't find much evidence against, but it's easier to describe the hypersphere.

Another interesting (and somewhat off-topic) property of a hypersphere is that if you were standing on one that was small enough, you'd see an infinite number of people standing behind and in front of you that looked exactly like you. You could take a step forward, and you would see your "clones" do the same. You could tap the person in front of you on the shoulder, but just as you did that, you would feel a tap on your own shoulder. Why? Because all of these people are YOU! You could step forward three feet and be at the same place you started. Of course, it wouldn't seem that way to you, because from a 3-dimensional perspective, it would appear to be a boundless space.

Much of this information (and, most likely, butchered facts) was taken from the book Hyperspace by Michio Kaku. A very good read if you're interested in this stuff.