RFC2554 describes the currently approved method for SMTP authentication. One part of this method is to add the AUTH= extension to the MAIL FROM: command for ESMTP. This A line in the qf file is used to store the value passed in that parameter.

If you compiled sendmail with SASL defined (SASL), this value will be the actual value passed by the AUTH=. Otherwise it is the value of $f ($f) normalized to the local domain if $f lacks a domain.