What, in Space, is warped?

What is being warped is something called the "metric" of space-time. Just like "the metric system" of units, a metric is how diplacements in space and intervals of time are measured and related to each other. For example, the Pythagorean theorem is a relationship between the lenght of the hypotenus c of a right triangle and its other two sides a and b (c^2=a^2+b^2). That is actually only true in Euclidean (aka "flat") space. Space is said to be "warped" if that relationship is not valid for actual measurements of displacements within it.