This shift is profound. To bring out the contrast, let me recall the situation in Newtonian physics. It is like a stage, an unchanging backdrop for all of physics. In general relativity, by contrast, the situation is very different. Einstein's equations tell us that matter curves space.
Geometry is no longer immune to change.
It reacts to matter. It is dynamical. Geometry is a physical entity, very much like matter. Now, the physics of this century has shown us that matter has constituents and the 3-dimensional objects we perceive as solids are in fact made of atoms. The continuum description of matter is an approximation which succeeds brilliantly in the macroscopic regime but fails hopelessly at the atomic scale.