Please kindly check the article, http://intersoftpt.wordpress.com/2010/12/16/coming-in-r2-mvvm-localization-manager-multi-bindings/, in the official blog of Intersoft.

The observable resource is implemented as a model, and consumed in the ViewModel. The observable resource can be defined through a generic template constructor shown below.

public class MyAppResource : Intersoft.Client.Framework.ObservableResource<Resources>
{
    public MyAppResource()
        : base(new Resources())
    {
    }
}
For more detail information and sample, please refer to the article link above.
Please let us know whether this helps or not.

I have read all the articles and documentation about the localization manager. My question was specifically about the overrides functionality, which none of the articles or documentation explain. 

Below is the line of code that responsible for the language change in the sample that available in the blog article.

private void ExecuteChangeLanguage(object parameter)
{
    LocalizationManager.Culture = new CultureInfo(parameter.ToString());
    this.TodayDateFormatted = TodayDate.ToString("D");
}

ClientUI Localization Manager is a framework that enables you to build dynamic, reliable localized applications. It overcomes the limitations of the Silverlight's built-in localization feature and packed with advanced features such as dynamic localized resource updating, MVVM design pattern support, and more.

The LocalizationManager contains the core implementation that processes the culture changes and consequently notifies the active observable resources. The ObservableResource<T> class implements IObservableResource interface to provide capability to track and monitor whether a localized resource has changed, which automatically updates the source elements on which the resource was bound to.

The overrides functionality is handled internally inside the Intersoft ClientUI Framework.

Hope this helps.