Stamp Duty is effectively a tax levied by the State Government on the transfer of assets. Every time you buy a car, shares in a company, and property you must pay an amount of money to the State Government based on the market value of the property. The State Government ensures that you pay stamp duty by refusing to register the transfer of property into your name before the stamp duty is paid and endorsed on the transfer. This is why solicitors require you to pay the amount of stamp duty to them prior to the settlement date so that they can ensure that at settlement the transfer is stamped.
Some of the larger conveyancing firms have the ability to receive stamp duty money at their office, thus allowing them to receive the legal expenses at settlement. It was intended that the GST would allow stamp duty to be abolished, but this is yet to happen.