Why isn't it just called Aerodrome Forecast? Where does the "terminal" part come from?
Terminal refers to the airspace near the airport, more or less similar to the ATC usage of terminal as in "terminal airspace" or area. TAFs cover the airspace in a 5 mi radius of an aerodrome, the immediate terminal area. The T in METAR also refers to terminal as in "Meteorological Terminal Aviation Routine Weather Report".