Liability refers to money that is owed to another party. Liabilities include debt (if you’re the borrower) and deposits (if you’re the bank). Assets must balance liabilities on a balance sheet.
Consider the balance sheet of a bank. On its asset side, it may have $45 billion in loans issued and $5 billion in reserves/cash. On its liability side, it may have $10 billion in outstanding bonds issued, $5 billion that they have borrowed from other banks, and $20 billion in deposits (deposits count as liabilities since they are money that is owed to the depositor; if the bank just places the deposit in a vault then the deposit counts as a liability while the cash counts as an asset and it balances). The difference between the assets ($50 billion) and liabilities ($35 billion) is the value of its equity and counts as a liability on the balance sheet. As a result, the two balance out.