The most common use of field functions is examining the solution. You might, for example, display pressure on the wall of a body. In this case, Pressure is a field function that has been defined by the system.
A more advanced use of field functions is the specification of boundary and region values as well as initial conditions. In this case you will typically define a new field function and apply it. An example would be writing a function for a parabolic velocity profile that is a function of the y-coordinate and using it for the inlet velocity at a boundary.