You have the option to cancel your clients' bookings, however, they can also do it themselves.
Once they are on your Storefront, they have to click on My bookings tab.
There they have to find the activity they want to cancel and click on manage booking and then cancel booking.
They can then click yes on the confirmation screen and the booking will be cancelled.
Note: PAYG bookings can only be rescheduled, not cancelled. Your clients will get a ticket back or not depending on the cancellation policy you set up.