“Do you want the application “Office365Service.app” to accept incoming network connections?”

3. If you are using Outlook and you don't accept network connections Outlook will not work correctly. Office365 is a network system, refusing it access to the network is not helpful.

If you're on a private network behind a router, the firewall serves no purpose. Turn it off in the Security & Privacy preference pane.

It is likely that Office365Service.app is not itself anything to do with Outlook or Word/Excel/Powerpoint but is probably checking for possible licensing abuses, it is therefore 'listening' to see if there are other copies of Office365 being used on the network and would then check to see if they are in breach of your license terms.

Office for Mac (not the 365 subscription version) does much the same thing.

With Office 2008 for Mac I find that even if you click allow and also make sure Office is listed as approved in the Macs firewall settings it will keep asking the same question each time you launch Word/Excel/etc. for Office 2011 this seems to work better in that it does not keep nagging once you save the setting.

Turning off the Macs built-in firewall would certainly stop any nagging messages. If you are using a desktop computer and your network has its own firewall then this is probably reasonably safe to do, if you have a laptop and use it out of the office then it is considered good security practise to always have the firewall turned on.

John Lockwood wrote:

It is likely that Office365Service.app

No need for "likely"

Per Microsoft:

Office 365 service administrators can connect to their

organization’s Office 365 service status from wherever they are with the Office

365 Admin app. The new app enables administrators to view service health

information and maintenance status updates from their mobile device. They can also

filter information by service subscriptions and configure app data refresh

intervals.