When added to a QuestVarTrap, this property changes the value of the specified quest variable. E.g. =3:thingy will set the value of thingy to 3. If the object is turned off, the variable will revert to its previous value. For another example, =1:goal_state_2 will make goal 2 become complete.
When added to a QuestVarTrigger, the property determines the conditions under which the object will send a TurnOn message down its ControlDevice links. The message will be sent once when the condition first becomes true. TurnOff will be sent if the conditions become false. E.g. If the value is =1:goal_state_4, TurnOn will be sent as soon as goal 4 is been completed.
A more comprehensive explanation of the uses of this property can be found here.
In Thief 2, this property can be added to a book, to allow it to show a different .str file depending on the value of a quest variable. E.g. If the Book→Text property is castle, and the value of Trap→Quest Var is difficulty, on Normal, the book will display the contents of castle0.str, or castle2.str on Expert.