It is a type of liability that comes into effect only under certain specified circumstances. In a contract, a contingent liability is set up to cover a situation that might happen or become known in the future.
As an example, in a real estate sale contract, there may be contingent liability around environmental hazards that are unknown at the time of sale, but existed prior to the sale.
In this case, the prior owner may retain a contingent liability exposure even though the property ownership has changed hands. It depends on the terms of the contract of sale.