No one here knows why your return was rejected. No one else can see the email you received telling you the return was rejected. But that email also has a rejection code or rejection message that YOU can see. What does it say?
If you didn't get the emails with the rejection notice, also check your spam/junk folders and other email accounts. Then log into your online account. Is there a "Fix My Return" button? If so, when you click that, does it tell you what is wrong?
Otherwise, you'll need to phone TurboTax Support, and they can tell you the reason for the rejection. They can also tell you how to fix it. Then you can resubmit the efile.
Hours are 5AM-5PM Pacific (8AM-8PM Eastern) Monday-Friday
FAQ: What is the TurboTax phone number?
If you are using Free Edition without PLUS, then you won't have phone support. If that's your situation, then you can contact a Support agent directly using messaging at Twitter or Facebook.