The symmetry is called general covariance or diffeomorphism invariance and it says that the dynamical equations of the gravitational field and any matter must be unchanged in form under any smooth transformation of spacetime coordinates.
The symmetry is called general covariance. The symmetry is called diffeomorphism invariance. The dynamical equations of the gravitational field and any matter must be unchanged in form under any smooth transformation of spacetime coordinates. This is what it says.