A property is under contract once the seller has accepted a buyer's offer and both parties have signed the purchase agreement, but the sale has not yet closed. The deal is legally binding, subject to any contingencies still to be satisfied.
During this period, the parties work through inspections, appraisal, financing, and title review. Many things must still go right before the transaction becomes final, so an under-contract status does not guarantee the sale will complete.
In MLS terms, an under-contract listing is often shown as pending or contingent depending on whether contingencies remain. Buyers can sometimes still submit backup offers on a home that is under contract in case the primary deal falls through.