The adorned element in this case is the Text Box control itself and you include an in the control template where you want to leave space for it.
The template above will cause the error message to be displayed in a Text Block below the Text Box.
The latter can for example be very useful for bindings in Styles and Control Templates and when you want to bind to some property in a parent element.
The Mode property of the , which is the default for the Text property of the Text Box control, the text you type into the Text Box does not update the source property until the control loses focus which happens when you click away from it. the setter for the bound property of the Data Context to get called, as the user is typing into the Text Box you set the Update Source Trigger property to enumeration.
A converter class converts data from one type to another during binding by implementing the Convert and Convert Back methods of the mentioned interface.