Agents constantly use this term incorrectly and flag it incorrectly in the MLS. If it is done correctly in the MLS, the property will move through various stages from active to closed. The include a/i, contingent and pending. Most of the time agents flag the property ctg (contingent) until it closes.
Once an offer is signed and accepted, it goes into a/i (attorney / inspection). During this time there is no written agreement. The sides are negotiating. If another offer comes in that is superior to the one that was accepted, it can bump the 1st offer out during this time.
Once the a/i period is closed, most properties move to the contingency period. This is because one side or the other needs something to happen (like securing a mortgage or selling a home). New buyers can still submit offers during this time. In some cases they are a backup. In other cases they force buyer #1 to forgo the contingency.
Once the property is pending it is just waiting for the paperwork to close.
Most agents do not like to bother with contingent properties because it is going to mean higher prices for the buyer. You are also doing a lot of legwork for little or no upside.
Broker Baird & Warner