Full Slate does not require clients to register for a user account to book appointments with you. This helps ensure more clients book online with your business by removing a barrier that will cause some clients to call or decide not to book. Clients are presented with an opportunity to register after they book an appointment (unless you've deactivated this option under Setup > Booking Details).
The benefits to clients of registering include not having to enter all their information each time they book an appointment, the ability to see all past and upcoming appointments, and a way to easily cancel and reschedule appointments.
You can determine if a client has registered for a Full Slate account by viewing their record under Clients > Details. At the top of the gray box on the right, it will either say "Not registered" or "Registered as firstname.lastname@example.org". If they have not registered, you can invite them to do so by sending them the 'Invite client to register' email template. Just go to their client record under Clients > Details, click 'Send message', select the 'Invite client to register' template and send.