Somewhere along the path, you were likely offered event notifications in a mail message or by a website, and accepted the offer.
That acceptance adds a subscribed calendar.
Should the registration for that subscribed calendar expires, connection messages will be displayed when the calendar is polled.
If you no longer wish to receive those notifications for the calendar, and/or if whoever was maintaining the subscribed calendar is no longer mai tai ing registrations, you will want to remove the subscribed calendar.
Here is how: Delete spam calendars and events on iPhone - Apple Support