What this means is that as you add children components to the MXML and you want the ActionScript Logic to manipulate them you have to make sure the ActionScript has them declared. To declare them you have to define properties in the ActionScript class whose name matches the component id you use in the MXML. For example, look at the Button id in the MXML above and notice that I have a public property in the ActionScript with the same name. The property must be public in the ActionScript class and you should mark them as [Bindable] so that if you have other components binding to them the change watcher system still operates as expected.
This works because the MXML file is an extension of the base logic class and the components with the matching id is equivalent to overriding the properties in the ActionScript. You may wonder why the properties have to be public and not protected if this is an override. The issue is that the MXML components are not part of the MXML class, they are children of the MXML class. Since they are children they do not have access to the ActionScript class’ protected methods and the compiler will see their id as a duplicate name for the MXML class, which is invalid. If the method is public, the compiler interprets this MXML component id as an override and it works. So, long story short… always make the properties [Bindable] public.