What is an incomplete payment? If I hit complete payment, will that charge the customer twice?

If a user closes the browser or didn't settle the payment after being redirected to the Payment Page, this will be logged as an Incomplete Payments. It will only be posted as a valid submission if the user completed the Payment and was able to completely process the transaction.

Payment can also be marked incomplete even if the payment was complete, this is usually caused by IPN not being enabled in PayPal:

https://www.jotform.com/help/276-How-to-Enable-IPN-for-Paypal

Completing incomplete submissions will not charge the user, regardless of if the payment was accepted or not.  Completing incomplete submissions will only trigger emails and place the data in with the rest of the form data.  No payments are processed when completing incomplete submissions.