The Jargon File (version 4.4.7, 29 Dec 2003):

bounce message
 n.

    [common] Notification message returned to sender by a site unable to relay
    email to the intended Internet address recipient or the next link in a 
    bang path (see bounce, sense 1). Reasons might include a nonexistent or
    misspelled username or a down relay site. Bounce messages can themselves
    fail, with occasionally ugly results; see sorcerer's apprentice mode and
    software laser. The terms bounce mail and barfmail are also common.


The Free On-line Dictionary of Computing (30 December 2018):

bounce message

   A notification message returned to the sender by a site unable
   to relay e-mail to the intended recipient or the next link
   in a bang path.  Reasons might include a nonexistent or
   misspelled user name or a down relay site.  Bounce messages
   can themselves fail, with occasionally ugly results; see
   sorcerer's apprentice mode and software laser.  The terms
   "bounce mail" and "barfmail" are also common.

   [Jargon File]

   (1994-11-29)