When I offer a subscription payment, what date will the payment be debited from the bank account (or PayPal account ) of the person paying?

The payment will be taken at the moment of the submission, then the payments will be taken since this date based on the configured schedule, so if it's monthly and the user submits the form today, the next charge will be on Sept 7, 2019. 

Here's also a guide with more info about subscriptions: https://www.jotform.com/help/166-How-to-Setup-a-Recurring-Payment-Option