Form-based authentication is a term of art in the context of Web- and Internet-based online networked computer systems. In general, it refers to the notion of a user being presented with an editable "form" to fill in and submit in order to log in to some system or service. However, the term is actually ambiguous in that the notion of using some sort of displayed "form" in which one enters credential information is a technique that is not unique to the Web.
Questions having the forms-authentication tag regards the authentication process in a form in general.
Reference: Wikipedia - Form-based authentication