There is no requirement to print out the approved ESTA application and take it with you on your journey. However, it is recommended to print out this application or at least photograph it with your mobile phone to be able to present proof at any time during the trip. In exceptional cases, airlines may request a printed ESTA permit prior to departure to the United States.
However, if you have forgotten to print or photograph your ESTA permit, you can also retrieve your ESTA application online in an emergency, stating your name, date of birth, passport number and country of issue of your passport.