Liabilities are anything that you owe (debt).
Why It's Important
It is important to know what liabilities are on your personal balance sheet because it allows you to make sure you are current with your bills and obligations. Yes, this includes items that are on your credit report! If you don't know what you owe, how could you possibly get rid of it?!
Businesses break liabilities down to two categories, current and long-term. Current liabilities are any debts that are payable within one year while long-term liabilities are payable over longer periods. To translate this to personal finance, short term liabilities would be your credit card balances (hopefully) and small loans. Long-term liabilities would be your car and your mortgage.
Knowing what liabilities you hold also allows you to calculate your net worth as I did for myself here.
The formula is Assets - Liabilities = Net Worth.