public void Test()
{
    Button theButton = button1 as Button;

    if (theButton != null)
    {
        // Checking if this thread has access to the object.
        if (theButton.Dispatcher.CheckAccess()) //<--- MYSTERY
        {
            // This thread has access so it can update the UI thread.
            theButton.Content = "Hello";
        }
        else
        {
            // This thread does not have access to the UI thread.
            // Place the update method on the Dispatcher of the UI thread.
            theButton.Dispatcher.BeginInvoke(DispatcherPriority.Normal,
            (Action)(() => { theButton.Content = "Hello"; }));
        }
    }
}