A four-digit number that is assigned to each newly filed patent application. The confirmation number, in combination with the application number, is used to verify the accuracy of the application number placed on correspondence filed with the Office to avoid misidentification of an application due to a transposition error (misplaced digits) in the application number. The Office recommends that applicants include the application's confirmation number (in addition to the application number) on all correspondence submitted to the Office concerning the application.
-- see MPEP 503 for more.
Source: U.S. Patent and Trademark Office.