Exchange of contracts is when the sale between seller and buyer becomes legally binding. At auction, this will usually be upon the fall of the gavel, after which documentation is signed by the purchaser and the deposit is taken by the auctioneer as the agent for the seller. Once contracts are exchanged, the buyer is committed to purchase the property.
Within the terms of the contract will be the completion date. This is the date on which title ownership of the property is transferred by the seller to the buyer, and the buyer takes possession of the property having paid over the balance of the monies. Once completion is confirmed by the solicitors, the buyer would then be able to collect the keys and move in.