A contingent liability is a potential liability. This means that the contingent liability might become an actual liability and a loss, or it might not. It depends on something in the future.
If your parent guarantees your loan, your parent will have a contingent liability. Your parent will have an actual liability and a loss only if you do not make the payments on the loan. On the other hand, if you make the loan payments, your parent will not have a liability and loss.
A $100,000 lawsuit filed against your company is a contingent liability (or loss contingency). Your company will have a liability and a loss only if your company is found guilty. If your company proves that it is not guilty, the contingent liability will not become an actual liability and loss.
Another example of a contingent liability is a product warranty. If a company promised to replace a defective unit at no cost to the customer within one year of purchase, the company will have an actual liability only if units are defective. If the company is certain that no units will be returned as defective, the company will have no liability and no warranty expense.