I read that most scientists believe that the Universe is either infinitely flat or pringle-shaped flat, and that doesn't make sense with me. I don't understand how our 3 dimensional world could be a part of a 2 dimensional universe.
Hi mtv22, welcome to physics forums!
That's not what is meant by 'flat'---they're using the term to describe higher dimensions (namely 3+1 space-time).
For the http://en.wikipedia.org/wiki/Shape_of_the_universe" [Broken] flat means asymptotically euclidean. Instead of having intrinsic curvature, the universe would be a perfectly flat, rectilinear grid (like you use in Cartesian geometry), where the interior angles of triangles add to 180 degrees, etc etc.
A lot of people ask this, and it's confusing because it's not always made clear that the term "flat" is jargon for "Euclidean." Granted, they call it flat because it implies the absence of "curvature", but the term curvature itself is something that has a very specific definition. Either way, it does not mean two-dimensional! We should probably add something about this to the Cosmology FAQ.