If you are allowing attendees to cancel their own registration in an event, the attendee can cancel by first amending their registration, then clicking "Cancel Registration" on the check out page.
Canceling a registration
Go to People > Registrations
Click to "Edit" the registration you want to cancel (double click the record or click the "Edit" icon)
On the check out page, click the "Cancel Registration" button
Confirm the cancellation and choose whether to send a cancellation email to the attendee (if unchecked, the attendee will not be made aware of the cancellation)
The record has now been cancelled. The "total amount" may update if any cancellation fees were used in the event
Note: Once a registration is cancelled, the cancellation cannot be undone. The attendee must register again or an event manager can create an admin registration.