The appointment screen will refresh each time you open the appointments module. If the appointments module is left open, it can automatically refresh at a given interval. So, if you leave your appointment module open on one computer and someone else books an appointment, that appointment will become visible on your open appointments page when the screen refreshes. You can set how often that happens in the branches tab.

Put the refresh time, in seconds, in the box. If you put zero in to turn this feature off, an open appointments page will not reflect new appointments booked, or appointment changes until you either make a change on that computer or you exit the page.