To allow customers to cancel their bookings on the booking site you can enable the setting "Allow cancellations by customer" in the booking site settings. This will give the customer an option to cancel a booking when they view a booking on the booking site. Bookings can be cancelled upon the time of booking unless you add a cancellation period. You can adjust the cancellation period relative to the start of the booking, for example to allow bookings until 2 days before the booking just add "2 days before" to the "Cancellation period" setting.
When a customer cancels a booking you will be notified via email if you have enabled email notifications.