Liquidated debts are liabilities for which the amount owed is certain. Most debts are liquidated debts, such as credit cards, mortgages, car loans, personal loans, and medical bills. Such creditors make it easy to determine the amount owed because they usually send monthly statements specifying the charges, accrued interest, fees, payments made, and the balance.
Unliquidated debts are liabilities for which the amount owed can not yet be ascertained. In other words, you know you owe someone money but the exact amount has not been determined. For example, if you are a party to a lawsuit and you will definitely owe someone money for damages, but the jury has not yet determined the amount of damages, the judgment is an unliquidated debt. The debt will become a liquidated debt when the jury determines the value of the damages.
Note that an unliquidated debt is not the same as a contingent debt (which is a liability that may or may not arise depending on the happening of a future occurrence) or a disputed debt (which is a liability that you and the creditor do not agree upon, either as to the amount owed or whether you owe it at all).