Payment fields are form action fields that direct a user to a third party payment provider. Users are then redirected back to your site with a status code indicating whether the payment was successful or not.
These field types are not part of the standard form family, they must be purchased separately, or as part of a solution we have developed, like Bookings.
There's a technical introduction to payment fields, including how the actions are processed and how to handle the responses returned from payment providers, in the knowledge base article - Using the Form Payment Fields.
Sensitive Documentation
Because the payment field documentation contains security information, it's not published on this site. Full documentation, usually a PDF, is provided for each payment field type when purchased. As the support team for a copy. The articles below give a high-level overview.