The anthropological meaning has been taken over into sociobiology, where the term polygyny is used to refer to a mating system in which a male has a more or less stable breeding relationship with more than one female, but the females are only bonded to a single male. In eusocial insects it refers to situations where colonies have multiple queens.
Note that in both the human and the animal situations, either the male or the female may at times copulate with additional partners; "polygyny" describes the formal or persistent relationships that help structure the society rather than being an exhaustive description of actual behaviour.