Network Functions Virtualization (NFV) is a specification (not a formal standard) from (primarily) communications industry service providers. The intent is to migrate many network functions (components) from physical appliances to virtual machine implementations.
For example, rather than having to deploy a new box for every instance of a firewall, (including rack space, power/cooling, cabling, etc), NFV prescribes the use of standardized virtual machine images (virtual appliances) to provide the required functionality. This would allow network communications providers utilize the same methodologies employed by cloud computing providers. There are many network product vendors today that deliver their products as a virtual appliance, but I am not yet sure they qualify as an “NFV” product.
The NFV specifications are maintained under the European Telecommunications Standards Institute (ETSI) Industry Specification Group (ISG). NFV is not a standard, but a specification for how networking functions will be virtualized.
NFV and SDN are closely related, but NFV does not require SDN. They are complimentary technologies. SDN can utilize NFV and vice-versa, but neither is required to have the other.
Closely related acronym; NaaS (to be defined later)
(This post has been edited to add a link to the NaaS entry)