In order to e-file you need to go through all of the steps of the FILE section until you come a big orange button that says "Transmit my returns now" and click the button. Until you do that, you have not filed your tax return.
When you e-file your return you will get two emails from TurboTax. The first one will say your return has been transmitted; the second one will tell you the IRS has accepted or rejected your federal e-file. If you filed a state return, there will be a third email (usually a day or two later) that tells you if the state e-file was accepted or rejected.
Check your e-file status:
https://turbotax.intuit.com/tax-tools/efile-status-lookup/