In general terms, this is the total area enclosed by the external walls of a building, measured to the internal face of those walls and taking into account every floor in the building.
This is comprehensively defined by the Royal Institute of Chartered Surveyors:
http://www.rics.org/uk/knowledge/bcis/about-bcis/forms-and-documents/gross-internal-floor-area-gifa-and-ipms-for-offices/