Spacetime curvature is the bending of spacetime’s geometry caused by the presence of mass and energy, and it is what general relativity identifies as the true source of gravity. Rather than treating gravity as a force pulling objects toward each other, general relativity treats it as objects simply following the straightest available paths through a spacetime that has been warped by nearby matter.
The amount of curvature at any point is governed by Einstein’s field equations, which relate the curvature directly to how much matter and energy are present there. More mass concentrated in a smaller region produces sharper curvature, which is why the spacetime near a black hole is curved far more severely than the spacetime near a planet.
Curvature is also two-way: matter tells spacetime how to curve, and that curvature in turn tells matter how to move, a relationship often summarised as Einstein’s central insight into gravity.