The monitor output button lets you preview the current Viewer image on an external broadcast video monitor.
You can select the external device and the display mode to use in the Viewer settings. To open the Viewer settings, press S on the Viewer.
NOTE: This option requires additional hardware, such as a monitor output card or a FireWire port.
For more information, see Previewing on an External Broadcast Video Monitor the Previews and Rendering chapter of the Nuke User Guide.