"Server" refers to using the application as the primary host with networked clients connected to it.
The default option for executing the application is to execute it as a "server". You then have the option of connecting clients.
The server sends the necessary data to all connected clients so that they display the appropriate console dashboards and overlays, fire the proper alerts, play the appropriate audios, etc.
If you aren't using networking, the server will just sit there in "standalone" mode without any networking overhead.
For details on how to configure and use the networking features of Dr. Neau's Tournament Manager, please refer to the networking topic.