how is it usually described or defined??
i googled this whicha int much:
The Weyl tensor has the special property that it is invariant under conformal changes to the metric. That is, if g' = f g for some positive scalar function then W' = W. For this reason the Weyl tensor is also called the conformal tensor. It follows that a necessary condition for a Riemannian manifold to be conformally flat is that the Weyl tensor vanish. It turns out that in dimensions >= 4 this condition is sufficient as well