Public ReadOnly Property Description As String

public string Description {get;}

<Grid x:Name="LayoutRoot">
  
  <!-- Add a Map Control. Set its Initial Extent to Deleware. -->
  <esri:Map Background="White" HorizontalAlignment="Left" Margin="0,180,0,0" Name="Map1" 
          VerticalAlignment="Top" Height="300" Width="400" Extent="-76.49,38.33,-74.37,39.92">
  
    <!-- Define an ArcGISDynamicMapServiceLayer. -->
    <esri:ArcGISDynamicMapServiceLayer 
          Url="http://sampleserver1.arcgisonline.com:80/arcgis/rest/services/Specialty/ESRI_StateCityHighway_USA/MapServer"
          Initialized="ArcGISDynamicMapServiceLayer_Initialized"/>
    
  </esri:Map>
  
  <!-- Description (Read Only). -->
  <sdk:Label Height="24" HorizontalAlignment="Left" Margin="0,88,0,0" Name="Label_Description" 
             VerticalAlignment="Top" Width="120" Content="Description:"/>
  <TextBox Height="69" HorizontalAlignment="Left" Margin="0,105,0,0" Name="TextBox_Description" 
           VerticalAlignment="Top" Width="400" TextWrapping="Wrap" />
  
  <!-- 
  As an alternative you could bind the ArcGISDynamicMapServiceLayer.Description directly to the
  TextBox.Text Property and not need to put any code in the code-behind for the 
  ArcGISDynamicMapServiceLayer.Initialized Event.
  -->
  <!--<TextBox Height="69" HorizontalAlignment="Left" Margin="0,105,0,0" Name="TextBox_Description" TextWrapping="Wrap"
           VerticalAlignment="Top" Width="400" Text="{Binding ElementName=Map1, Path=Layers[0].Descripton}"/>-->
  
  <!-- Provide the instructions on how to use the sample code. -->
  <TextBlock Height="52" HorizontalAlignment="Left" Name="TextBlock1" VerticalAlignment="Top" Width="400" 
       TextWrapping="Wrap" Text="When the ArcGISDynamicMapServiceLayer Initializes the Description
       will be automatically populated in the TextBlock." />
      
</Grid>

private void ArcGISDynamicMapServiceLayer_Initialized(object sender, System.EventArgs e)
{
  // Get the first layer in the Map. 
  ESRI.ArcGIS.Client.ArcGISDynamicMapServiceLayer myArcGISDynamicMapServiceLayer = null;
  myArcGISDynamicMapServiceLayer = (ESRI.ArcGIS.Client.ArcGISDynamicMapServiceLayer)(Map1.Layers[0]);
  
  // Description (Read Only).
  // NOTE: The Description information is set in the Description section on the General tab of the Data Frame 
  // Properties dialog in ArcMap.
  TextBox_Description.Text = myArcGISDynamicMapServiceLayer.Description;
}

Private Sub ArcGISDynamicMapServiceLayer_Initialized(ByVal sender As System.Object, ByVal e As System.EventArgs)
  
  ' Get the first layer in the Map. 
  Dim myArcGISDynamicMapServiceLayer As ESRI.ArcGIS.Client.ArcGISDynamicMapServiceLayer
  myArcGISDynamicMapServiceLayer = CType(Map1.Layers.Item(0), ESRI.ArcGIS.Client.ArcGISDynamicMapServiceLayer)
  
  ' Description (Read Only).
  ' NOTE: The Description information is set in the Description section on the General tab of the Data Frame 
  ' Properties dialog in ArcMap.
  TextBox_Description.Text = myArcGISDynamicMapServiceLayer.Description
  
End Sub