Background-independence is the requirement that the theory be formulated based only on a bare differentiable manifold but not on any prior geometry. General relativity is the first example of such a theory. This is a radical shift as all theories before General relativity had part of their formulation a pre-existing geometry, e.g. Maxwell's equations are based on Minkowski spacetime. All perturbative string theories are based on a prior background geometry (by the very definition of perturbative). So perturbative string theory is not background independent. But some people then claim that perturbative string theory is just non-manifestly background independent, as if background independence is being gauge fixed...but string theories on distinct background geometries are obviously physically distinct situations, so how can they be related to each other by a gauge transformation?