Debts include mortgages, car loans, large outstanding credit card bills, and so forth.
It is not necessary to list new estate expenses as debts: you can simply record payment of estate expenses via the Cashflow tab as they arise. If you do want to record estate expenses as debts, be sure to leave the Owed at Death column blank.
Debts to the estate are considered assets, and should be entered as Loans on the Asset tab, not here.
You can delete a debt from the Debts tab by selecting its row and then pressing the Delete button at the top of the tab.
Do NOT delete a debt just because it has been paid or forgiven. Only delete debts that were created by mistake. If you delete a valid debt, EstateExec will no longer be able to generate accurate Inventory Reports from the time of death, or a Final Accounting Report that shows changes to the estate over time. Moreover, when you delete a debt, all references to it will be deleted, including any debt payments.
If you want to see just the current debts of an estate, simply filter the Debts table to include only those with a Owed Now > 0.