Appointments can be deleted completely, and they won't be visible in a clients history.
If you want to remove an appointment completely and permanently, you can. This means you won't be able to see the appointment in your clients history and the appointment is permanently deleted and can't be recovered. If you'd like to keep a record of a canceled appointment, choose to Cancel it instead!
You can do this on the Calendar, Appointment or Clients pages - they all work in a similar way: