You can delete an appointment straight from the calendar. You need the permission to edit appointments.
Step 1 — Open the appointment
Tap the appointment in the calendar. The quick-actions bar appears.
Step 2 — Delete
Tap "Delete" and confirm.
If the appointment is part of a recurring series, you'll be asked whether you want to delete just this appointment or all of them in the series.
Note: if you want to keep the appointment but mark that it didn't happen, it's better to use the "Canceled" or "No show" status instead of deleting it — that way it stays in the history.