Geodesic Deviation is the General Relativistic Phenomenon that answers the many letters from student spacefarers who wonder why their spaceships make a foreboding creaking sound each time they fly through a wormhole! The Geodesic Deviation Equation — a particular definition of the Riemann Curvature Tensor, tells us why and how much creaking to expect. Or, more importantly, whether you'll survive traversal at all!
We've already seen several different meanings of curvature as in introduction: