This is a purchase made at a shop in the international terminal of most airports which is free from taxes. Since some goods – like alcohol and cigarettes – are highly taxed, this can result in a steep discount on these items.
There are three separate concepts at work:
If you have checked in and presented your passport for an international flight, you are technically not “in” the host country anymore. You’re sort of in a “no man’s land,” thus a merchant can sell you things with no taxes applied. This is why many international airports have you walk through the duty free shopping area immediately after clearing security to get to your gate – at that point, you are “economically stateless.”
Countries have traditionally not taxed exported goods, in order to keep them competitive. Clearly, if you’re leaving the country, you can rightly claim that you’re exporting the good you just bought, and thus it should be free from taxes.
Many goods that result in negative societal effects – like tobacco and alcohol – are taxed heavily by governments to compensate for those costs. If you’re buying something to consume outside the borders of a country, then that country can’t claim a societal cost for which it needs to apply taxes.
You will often have to show your boarding pass to prove you are leaving the country and the items will be consumed elsewhere. Some airports will actually deliver the items to your gate as you board the plane. Other shops will package them in sealed, clear bags, so that it’s clear they are unopened when you get on the plane.
You might still have to pay taxes on it when you come back to your home country. Technically you are required to “declare” purchases you made overseas and are bringing back to the United States.
The Customs and Border Patrol maintains a list of exemptions. For example, you bring can back up to 400 cigarettes and one liter of alcohol without paying import taxes on them. Other exemptions are based on the cost of the good, and the country in which you purchased it. In most cases, the exemption is currently $800.