The captcha setting is a toggle; when it's on, every card that a user can create, edit, comment on, or delete without signing in will require a captcha. Naturally, captchas are never required for signed-in users.
If you are hosting your own Wagn, you will need to register for ReCaptcha keys and add them to config/application.rb, like so:
config.recaptcha_public_key = '6LdhRssSAAAAAFfLt1Wkw43hoaA8RTIgso9-tvtc'
config.recaptcha_private_key = '6LdhRssSAAAAAGwzl069pJQBdmzCZigm1nV-dmqK'