The theory of comparative advantage shows how voluntary exchange benefits both parties and encourages specialization. You don’t need to possess an absolute advantage in any particular productive activity to enjoy a comparative advantage. Your comparative advantage is whatever you can do relatively cheaply compared to everything else and everyone else. For instance, Haiti still trades with the U.S. even though it’s a much poorer economy. The reason is that the U.S. worker focuses on her/his comparative advantage – making stuff like microchips, software, financial services, houses, retail, design, engineering services, accounting services, higher education services, wheat, corn, soybeans, apricots, and airplanes – and leaves other stuff for workers in other countries, like making t-shirts, steel, rubber, bananas, coconuts, furniture, and toys. Haiti, in particular, specializes in making t-shirts. An American worker could probably make more t-shirts than a Haitian one – we have better tools (more capital) – but it doesn’t pay for us to spend our time on that when we could be doing on the things aforementioned. So we buy t-shirts from Haiti instead.
At e3ne.org I have a new post up explaining the theory and offering a short quiz. I’ve copied it below. Feel free to take your shot at the answers in the comments!
1. Imagine you’re the chief executive of a successful information technology business. You rose through the ranks as a graphic designer and are very good at that, but you’re also a good manager and fundraiser. Your task now is to write up an annual report for the shareholders. Should you use your graphic design skills to format an excellent annual report, or should you simply type up the information and delegate the formatting of the report to one of your employees?
2. Imagine the U.S. opens up to imports of clothing from China. What happens to the price of clothing in the U.S. and in China?
3. Does opening up to Chinese clothing affect the quantity of U.S. exports, say, of microchips?
4. Does opening up to Chinese clothing affect the price of microchips in the U.S. and in China?
PILEUS 
1) You should delegate the formatting for the simple reason that the cost you incur in terms of forgone management or fundraising is higher than the cost you incur by not formatting the report. This, of course, assumes you do not derive a high nonpecuniary benefit from formatting documents.
2) The price of clothing in the US should decrease as competition forces US manufactures to lower prices and Chinese comparative advantage in clothing production enables US consumers to purchase more for less. In China the affects is likely ambiguous or a rise in prices as producers shift production to export markets thereby reducing domestic supply relative to demand and pushing up prices.
3) The important distinction here is whether the products are in competitive or complementary industries. Assuming we are talking about clothing and microchips, increased Chinese exports are apt to increase American exports given that Chinese domestic consumers will have more income due to gains from trade to purchase US microchips.
4) The key question here is whether we are ignoring the impact trade can have on exchange rates. Absent exchange effects, US microchip prices could rise again because production for export reduces domestic supply relative to domestic demand. In China, this affect is highly conditioned on exchange rate effects. Increased Chinese clothing exports will push up the value of the Yuan making US microchips cheaper. Absent exchange rate movements, the price of US microchips in China would likely be constant or fall slightly owing to the gains from trade; but this is contingent on whether Chinese firms were producing microchips for domestic consumption at higher cost.
Nailed it!