  For a conformal manifold, we describe a new relation between the ambient
obstruction tensor of Fefferman and Graham and the holonomy of the normal
conformal Cartan connection. This relation allows us to prove several results
on the vanishing and the rank of the obstruction tensor, for example for
conformal structures admitting twistor spinors or normal conformal Killing
forms. As our main tool we introduce the notion of a conformal holonomy
distribution and show that its integrability is closely related to the
exceptional conformal structures in dimensions five and six that were found by
Nurowski and Bryant.
