Martha Stewart, let us agree, can iron shirts better and in less time than anyone else in the world. So, does it make sense for Martha Stewart to iron her own shirts? No!

Every hour that Martha spends ironing shirts is an hour that she doesn't devote to running her billion dollar business--thus ironing shirts has a high opportunity cost for Martha. Since Martha's opportunity cost of ironing shirts is high it pays her to run her business and use the proceeds to trade with someone else who will iron her shirts. Even though Martha has an absolute advantage in ironing shirts we say she has a comparative advantage in running her business.

Importantly, note that this argument implies that no one can be the lowest (opportunity) cost producer of every good, precisely because the better you are at A the higher the opportunity cost of doing B. The same thing is true for countries as for people. Even if a country is better in an absolute sense at producing all goods it will still pay that country to specialize in what it is most best at, in its comparative advantage, and trade for other goods. Thus, the idea of comparative advantage is a deep reason explaining how trade can make people better off.

p.s. (It's not the only reason).