A contingent liability is a debt you might have but you don’t know for sure.
If someone sued you, you’ll have a debt if you lose. But you won’t know for sure until the case ends. You might have a liability. That is a contingent liability. If you guaranteed a loan for your son, you might have to pay if he doesn’t. But you won’t know until you find out if he paid. That is a contingent liability. If it’s looking like you will have to pay a contingent liability and you know how much it is, companies put it on their balance sheet. Otherwise they list it in the notes to the financial statements.