How is the Max Zero Fuel Weight used in calculating weight and balance?
Maximum Zero Fuel Weight is an operating limitation intended to protect the wing spar structure by limiting the concentration of load, relative to all up weight, borne by the wings in the middle of the span.  In other words it limits spar bending loads at the wing roots imposed by the mass in the fuselage because any additional weight must be in the wing tanks where the additional load doesn't add to root bending.  

Generically, Zero Fuel Weight can just mean all up weight minus usable fuel.  However, when an instruction says to use "Max Zero Fuel Weight" it's saying to apply a published MZFW value that is an operating limitation.  In your case you would enter the Max ZFW value from the airplane's Operating Limitations in the AFM into the app.