Tensors have an associated rank from zero to infinity. Scalars are in fact zero rank tensors.
Vectors are first rank tensors.
Second rank tensors are associated with anisotropic systems and often link cause and effect vectors. These two quantities are linked by the molecular polarizability, a second rank tensor. Out of these calculations, a myriad of molecular property tensors arises, each one of which seems to assume importance in at least one spectroscopic technique, however obscure. Much of the challenge of interpreting these phenomena lies in putting flesh and bones on the components of the tensors which all essentially involve the pesky infinite sums of perturbation theory.