The beginning of the paper

Wess, Julius, and Bruno Zumino. "Consequences of anomalous Ward identities." *Physics Letters B* 37.1 (1971): 95-97.

gives the answer.

It is known [1] that the naive or normal Ward identities are not always satisfied in renormalized perturbation theory. In other words, the Green's functions do not always satisfy the identities which correspond to invariance or partial invariance of the basic Lagrangian. In the case of the partial conservation equation for the axial vector current, anomalies occur if there are fundamental spinor fields in the theory. They are due to the singularities of the spinar triangle graph and, in the non-abelian case of SU(3)$\otimes$SU(3), of higher polygonal graphs. It is likely that the anomalies due to these single loop graphs are not modified by higher order many loop corrections.

In this note we observe that the anomalies must satisfy consistency or integrability relations which follow from the structure of the gauge group and which are non trivial in the case of nonabelian groups.

The anomalies (nonvanishing divergence terms) must match the integrability conditions listed on the top right of p.96. An arbitrary potential assignment of values to all these divergence terms is consistent (i.e., can possibly correspond to an anomaly) only if the assignments are chosen to satisfy these conditions. Thus one can consider these integrability conditions as well as consistency conditions. The abstract of the paper already introduces this terminology:

The anomalies of Ward identities are shown to satisfy consistency or integrability relations, which restrict their possible form.

The paper hep-th:0704-2472 mentioned by dimension10 interprets these consistency conditions in terms of cohomology.