An example of a gauge anomaly: an effect of quantum mechanics — usually a one-loop diagram — that invalidates the general covariance of general relativity combined with other fields.
It is related to the non-conservation of the energy-momentum tensor, ∇μ⟨Tμν⟩ ≠ 0.
General covariance is the basis of general relativity; the anomaly is precisely its breakdown in the quantum theory, tied to diffeomorphism symmetry.