The ability to express a theory consistently under arbitrary changes of spacetime coordinates. A tensor equation has this property when all its fields, including any background structures, transform appropriately. It does not by itself say that every active transformation is a dynamical symmetry, or that no preferred background structure exists. General relativity has the additional substantive feature that its metric tensor is dynamical.
General covariance is a principle from the field of theoretical physics and mathematics, particularly in the context of general relativity and differential geometry. It refers to the idea that the laws of physics should take the same form regardless of the coordinate system used to describe them. In other words, the equations that govern physical phenomena should be invariant under arbitrary smooth transformations of the coordinates.
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