A "Lay bet" is a bet for something NOT to happen, usually a Win. Betting exchanges make this type of bet possible by facilitating peer to peer contracts.
If you were to place a bet on Red Rum to NOT TO Win at the Grand National. You would be Laying the horse. When you place lay bets, you are essentially playing the role of bookmaker for that race. You must put up the liability needed to pay the "backers" should the horse win. If the horse doesn't win, you will keep the "backers" stakes.