The ZFW (Zero Fuel Weight) is just what it says;

The dry weight of the aircraft + the total Payload weight (Pass and cargo) = Zero Fuel Weight (ZFW) ;)

If you add the the fuel into the equation you now have the TGW (Total Gross Weight) or GRW (Gross Weight) of the aircraft.

The FMC knows how much fuel you have in the tanks so if you give it the ZFW it will calculate the TGW or GRW for you.

Just one last "term", TOW (Take Off Weight) this is basicly the TGW at the moment of take off. It is a good pilot that makes sure to never exceed the MTOW (Maximum Take Off Weight), because doing so might break your airplane in two! 8-)