a party is said to have a "comparative advantage" over another party in producing a good if it has a lower opportunity cost
when producing that good than the other party has, even if the other party has an absolute advantage
in producing that good.
For example, imagine that there are only two products in the world: guns and paperweights. Let us assume it costs the US $10 to produce one gun and $1 to produce one paperweight, and it costs New Zealand $15 dollars to produce one gun and $5 to produce one paperweight. In this situation, the US has an absolute advantage in the production of both guns and paperweights because it can produce either at a lower material cost than New Zealand. However, New Zealand has a comparative advantage in gun production because in terms of opportunity cost, it only costs New Zealand three paperweights to produce one gun while it costs the US ten paperweights to produce one gun. On the other hand, the US has a comparative advantage in paperweight production because it only costs the US 0.1 guns to produce one paperweight while it costs New Zealand 0.3 guns. Thus according to the Theory of Comparative Advantage, the US should only produce paperweights and New Zealand should only produce guns, assuming they are both willing to trade freely, and they will both come out ahead, getting more goods at a lower cost. Do the math - it works out for any combination of goods traded.
The concept of comparative advantage can be used to produce a strong argument for free trade, because as long as a nation has a comparative advantage over others in even one good (which they always do), they will benefit from trade.