A tax that is charged on the transfer of an asset. It is usually a percentage of the value of the asset. It can be a significant part of the cost of buying securities and property.
The advantages of stamp duty are that it is usually cheap and simple to collect, and hard to evade. For example, the sale of a house is a single large transaction, the calculation of stamp duty is simple, and the transaction cannot easily be hidden. Similarly, sales of securities through exchanges are done through system that automatically collect the tax, and even off market sales are usually ultimately registered (except in bearer securities).
The disadvantage of stamp duty when applied to financial transactions, is that by increasing the cost of transactions, it provides an incentive to limit trading, making markets less liquid and possibly even less efficient.
Many countries have either stamp duty, or very similar financial transactions taxes. A specific example of this would be a Tobin, or Robin Hood, Tax.