A contingent contract is one that is fully executed and binding but is contingent on an event happening. If the event does not happen, then the contract may be terminated by one of the parties as described in the contract.
Typical events that create a contingency are
1. sale of another house (owned by the buyer usually) - if the buyer's home doesn't sell, contract may be terminated.
2. approval by the seller's bank - in a short sale the seller's mortgage company may approve a different amount and the buyer can terminate the contract.
In these cases typically the buyer receives his earnest money back but may have paid for inspection, appraisal, survey or other charges and does not get that money back unless so provided in the contract.
The contingency may also be the type that the seller can force removal of. If, for example, the buyer's home does not sell and the buyer has a contingency for that, the seller may accept other offers without a contingency of the second buyer's house selling. If so, the first buyer with contingency can be notified that his contract will be kicked out unless he removes the contingency. Rather than call this a contingency contract, we call this a kick-out contract. Other buyers may propose contracts that effectively force the KO contract to be modified or terminated.
Other types of contingencies are possible.