The Publish button is used to push content updates and program instructions to each player.
To send updates to your players, click each player checkbox (#1) and click the Publish button located on the right, above the scheduling grid (#2).
You can send updates from the MONITORING window as well. To do so, open the monitoring window, then click each player checkbox (#1) and click the Publish button located to the right of the CLEAR ALERT button (#2).
The advantage is you can track the progress of the file transfer in real time (#3).