the Singleton Pattern helps you to store persistent data in your application, which should be globally accessible at any time. Therefore it is recommended to use a Singleton Class for your Model in a MVC-Application. For example your Singleton Class could hold the data of a loaded XML-File or in a game it could hold the score/bodycount of the player. The Singleton Pattern makes sure you can access that data whenever and whereever you want with a simple statement like this: _model = Singleton.getInstance();
The function getInstance() just returns always the same instance, which is just created once at the first function call.
I just updated the popular Flash/Actionscript Basic Model View Controller example. For the Model I use the Singleton Design Pattern, which makes it very easy to access data throughout the entire application.
You can see I just call Singleton.getInstance(); to access the Model with all its data.
check out the new AS3 example here: MVC Singleton Slideshow. you can view the actionscript source via right-click on the Flash Slideshow. alternatively feel free to download the entire flash builder project here.
I recommend this basic setup for tiny Flash applications, which will help you to keep your code structured and clean. For bigger Actionscript applications you should think about using a mvc framework - for example Robotlegs.