General relativity describes gravity as curvature of spacetime, not as a force acting at a distance. Matter and energy tell spacetime how to curve, and curved spacetime tells matter how to move.

Free-falling objects follow geodesics, the straightest possible paths in curved spacetime. These paths are the natural generalization of inertial motion.

A metric tells us how to measure spacetime intervals. In flat spacetime, the interval can be written as $$ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2,$$ while curved spacetime uses a more general metric.