Star Trek notwithstanding, this is what is meant by ``warped
space.'' Our apparently ``flat'' ( i.e. Euclidean) 3-D 
universe is embedded in a 4-D 
space called `` Minkowski space.'' Light always follows
a geodesic - the ``shortest'' distance between two points
constrained to a given 3-D hypersurface - and we can
tell if this hypersurface is curved in a 4-D analogy of the
curvature of the Earth's 2-D surface in 3-D, because if it is, Euclidean
geometry will fail.
This occurs (it turns out) in any gravitational field. Hence the terminology that has been popularized by various SF authors: ``Gravity warps space.''
Another way of putting this is to say that the metric of Minkowski space changes in a gravitational field. A detailed mathematics of tensor calculus has been worked out to describe this effect quantitatively; I don't understand a bit of it, so you will be spared.