In all but a couple of the TTASxxx objects this is the property you will use to connect the object to either a DEFINEd field in the program or a file. If you don't setup this property the display property for the object (generally TEXT) will not display anything unless you set it directly. The Field Name property value should be the exact same as the field name used in the program. For example, if you use BKAR.CUSTCODE in the program you would save BKAR.CUSTCODE to this property (case doesn't matter).
There is a Property Editor attached to this property that will allow you to choose a field from the data dictionary, or, if you have a program loaded in the Source Code Editor, it can also check for DEFINEd fields in that program.
NOTE: If you want the events for the object to fire (such as .PRE, .POST, .CHANGE, etc.) but you don't want the object attached to any specific field, you may do so by entering the value of NONE in this property. This will alert the runtime that you want this object to be active without a field in the background. To the user it will appear the same as any other object on the screen.