“Liability” can have several meanings in a legal context, primarily:
When a person or entity has a legal obligation to act or omit from acting in a specific manner, and if or when that person or entity breaks its legal obligation, they can be held legally liable. For example, all people who have a job in the United States are required to pay income tax. If a person does not pay their income tax, then they will then face all of the legal liability that comes with not paying their taxes.
If a person is in trouble financially and is forced into bankruptcy, they are legally obligated to list all of their assets in order for a court-appointed representative to review them, and they have to try to find a way to pay the liabilities over a longer time period at a decreased rate. Companies are legally obligated to list all of their financial liabilities for tax purposes and for accounting standards.