Definition

Action<int> example1 =
   (int x) => Console.WriteLine("Write {0}", x);
Action<int, int> example2 =
   (x, y) => Console.WriteLine("Write {0} and {1}", x, y);
Action example3 =  
   () => Console.WriteLine("Done");

using System.Windows.Threading;  // in WindowsBase.dll
 
public partial class MyWindow : Window
{
  public MyWindow()
  {
    InitializeComponent();
    new Thread (Work).Start();
  }
 
  void Work()
  {
    Thread.Sleep (5000);           // Simulate time-consuming task
    UpdateMessage ("The answer");
  }
 
  void UpdateMessage (string message)
  {
    Action action = () => txtMessage.Text = message;
    Dispatcher.Invoke (action);
  }
}

Source:

• Threading (Part 2): Rich Client Applications and Thread Affinity

///----------------------------------------------------------------------------------------
/// <summary>
/// Close the popup menu.
/// </summary>
///----------------------------------------------------------------------------------------
public void Close()
{
    //----------------------------------------------------------------------------
    // Deal with cross thread ownership of UI control instance
    // by invoking an action delegate. In other words, 
    // popupmnu is owned by thread that instantiated it (when Open() was called),
    // so we cannot close popmnu arbitrarily.  We need the help of
    // the owner thread's Dispatcher to execute the Close() for us.
    //----------------------------------------------------------------------------
    //Action action = () => popmnuReports.IsOpen = false;
    Action action = this.CloseDelegate();
    this.Dispatcher.BeginInvoke(action);
}
 
///----------------------------------------------------------------------------------------
/// <summary>
/// Close method deletegate, used by cross thread dispatcher.
/// </summary>
/// <returns></returns>
///----------------------------------------------------------------------------------------
private Action CloseDelegate()
{
    return delegate()
    {
        popmnuFitting.IsOpen = false;
        m_TimerForDisplay.Enabled = false;
    };
}

• DotNetPerls: Action
• MSDN: Action of Delete
• StackOverflow: Use of Action Delete in C#
• WPF UI Update from Background Threads