How can I execute code when value of a variable changes in C#?

You either have a reference to the GUI in your model (where the variable is) and directly perform the GUI change in the setter method, or you make your GUI observe your model via an observer, and have the observable model fire events to the observers in the setters. The former will lead to spaghetti code eventually, as you add more and more direct links between model and view, and thus should only be used for in-house tools and simple programs.