NERV (German for "nerve") is a special organization that was put together to combat the Angels after the Second Impact and is the organization responsible for the creation of the Evangelions.
NERV is an international organization with their center of operation located in the city of Tokyo-3, Japan. More specifically, they run the majority of their research and operations out of NERV Headquarters, a large facility located in the GeoFront. Outside of their main operation in Japan, NERV also has operations in the United States, Germany and possibly more.
As far as the world is concerned, NERV is under the control of the United Nations however the truth isn't so simple. In reality, the shadowy organization SEELE are in control of the United Nations and as such, they are also direct overseers to NERV. Despite this oversight, they still mostly operate as an independent organization with SEELE being their main source of funding.

As an orgnization, it is the successor to Gehirn and therefore the two organizations have a lot in common.