[ajkjk]

Picture curves on the surface of the earth. They seem flat locally, but if you go a mile north, a mile east, a mile south, and a mile west, you don't end up _exactly_ where you start. (In the northern hemisphere you end up a little east of where you start; in the southern, a little west.)

Same thing in general relativity: the metric tensor measures the failure of closed loops on each axis to not close perfectly, the way they would in Euclidean space.

Basically even as a small creature on earth you can 'figure out' about the curvature by carefully measuring small-ish loops. The same is true for spacetime, but the loops' deformities are even smaller.