The document that confirms that you have passed the check-in process successfully, and are permitted boarding the airplane is the boarding pass.
During the check-in, you will be issued a boarding pass. You can also receive a boarding pass during the online check-in before you go to the airport. (In case your airline sustains paperless boarding passes, you may have issues at the departure airport that may not have the proper equipment to handle them.)
In case the online check-in is not accessible, make sure you carry a printed version of your e-ticket to the airport so that a boarding pass will be released prior to departure.
