What does it mean a theory is the gauging of a current?

Question

What does it mean when people say that the Chern-Simons theory $$\mathcal{L}\sim\operatorname{Tr} \left(A\wedge dA+\frac{2}{3}A\wedge A\wedge A\right)$$ is the "gauging of the the topological current $\star F$ by $A$ itself", where the field strength is $F=dA+A\wedge A$? I would usually guess that people use "gauge" as a verb to mean, broadly speaking, adding a kinetic term for a gauge field to the action and changing $\partial_\mu\to D_\mu$, but in this context (the C-S action) I'm not sure what that would entail.