This is the legal part of the sales process when a property is sold by private treaty or auction. There are two copies of the contract, one for vendor and the other for the purchaser. The purchaser and vendor can negotiate changes to the terms in the contract prior to signing which can be done through their solicitor. Each party signs a copy and then they are exchanged (this is usually done by your solicitor or conveyancer). When the contracts exchange, the purchaser is required to pay a deposit on the property (usually 10% of the purchase price).
A purchaser is not legally bound to buy the property until signed copies of the contract are exchanged. The purchaser usually has a 5 day cooling off period in which they can withdraw from the sale after exchange has taken place. This cooling off period can be waved or extended by negotiation.
Vendors do not have a cooling off period, once the contracts have exchanged the vendors are bound to sell.