This option allows users to create accounts by themselves, via the "sign up" link on the top right shoulder of the page. Make sure to not grant significant permissions to authenticated users, as anyone on the network will be able to get them.

When this checkbox is unchecked, someone with the administrator role would have to create accounts.

By default, Jenkins does not use captcha verification if the user creates an account by themself. If you'd like to enable captcha verification, install a captcha support plugin, e.g. the Jenkins JCaptcha Plugin.