Either a Client or a Staff person can mark an appointment as "Cancelled". A client can do so by logging into the scheduler to manage his/her appointments or by clicking on the link in the New Appointment email they receive or the Appointment Reminder email.
Marking an appointment as Cancelled clears it from your calendar view to open that timeslot up for another person looking to schedule with you. All canceled appointments can be found by going to Appointments → Lists → Cancelled. It can also send out an email to the client and the staff about the cancelled appointment.
Cancelled appointments can be Re-Opened if a client cancelled in error, or they can be marked as Completed or No Show if you as a staff person accidentally categorized them incorrectly. Cancelled appointments can also be deleted (be careful, though, as this is a permanent action).
From the Appointment Detail page, you can see if an appointment is in Cancelled status by the red status listing: