The purpose of the button is to pause the Live Status updates to the web page. The live status updates are the log messages being displayed in real time on the screen for the various connections. This pause will not have any effect on the integration connection or task or syncing with your integrations. It only stops updating the screen in real time.
This is required at times when too many updates are being continuously shown on the web page because it prevents accessing any of the action menus for configuration.