When an Appointedd booking is modified, you have the option to send the customer an email to notify them that their booking has been modified.
Now, that email includes an .ics calendar file which will automatically update the original calendar file e.g. move it to the new date and/or time, update the location, change the service name.
So there's no manual calendar management required by the customer - it's all done for them!
To make sure that you're sending your customer an email when a booking is modified, switch on that setting here.