Filing bankruptcy means dealing with and understanding lots of different types of debt... you'll be told about secure and unsecured debt, dischargeable and non-dischargeable debt, and pre-petition and post-petition debt (just to name a few!). It can get pretty confusing.
The question of what constitutes "post-petition" debt is an important one. In short, post-petition debts are any debts you incur after filing bankruptcy. Post-petition debts are so important because they are generally not dischargeable (there is another type of debt popping up). They don't go away after bankruptcy.
If you open a new credit card account or take out a new car loan after filing bankruptcy, the bankruptcy does not eliminate that debt, even if you wish to return the property. If you borrow from a friend or family member, or get medical treatment after filing, you will probably be facing a post-petition debt. These post-petition creditors will be free to sue you after the bankruptcy automatic stay ends at the discharge of your case.
Beyond these obvious examples, there are some ongoing debts that may be considered post-petition debts. Utilities, phone and cable bills, and taxes will all be due after filing bankruptcy, even if the amount you owed before filing (PRE-petition debt) is discharged. Taxes will be due as always, so make sure you are prepared to pay them.
Your car and mortgage payments will continue after bankruptcy, assuming you wish to retain the property. In a Chapter 7 bankruptcy, the payment must be made as normal or the property can be repossessed or foreclosed upon. You must be current on these payments at the time of filing bankruptcy. In Chapter 13 bankruptcy, the payments will be made through the bankruptcy plan.
It is important to point out that debts accrued during your Chapter 13 bankruptcy plan (which lasts 3 to 5 years) are NOT discharged, even though you are technically "in bankruptcy". Once again, only the debts from before the date of filing are discharged. Not only will post-petition debts survive your Chapter 13 bankruptcy, you must also get Bankruptcy Court permission to take on certain post-petition obligations, such as a new car payment.
If you have any question about what constitutes a post-petition debt, be sure to clarify it with your attorney before filing.