I filed my tax return and the federal and state didn't accept my return. I am refiling again and Turbotax said that it won't charge me twice. So how does that work?

The fees you pay TurboTax are for preparation of your returns only.  E-filing is not a separate fee you need to pay.  If your returns are rejected, you can fix whatever is necessary without worrying about having to pay again.

You can attempt to e-file up to five times with the online software.  Afterwards, you will need to file by mail.