An absolute advantage means the ability of a nation or firm to produce more of a given good or service than another nation or firm. A comparative advantage is more complex, taking opportunity cost into account. What this means in practice is important. One example might be from the Cold War. During this conflict, it is often said that the United States prevailed because its economy was better able to sustain the cost of developing a massive military, including expensive nuclear missiles and other costly technology. The United States had an absolute advantage over the Soviet Union in the production of military equipment.
Comparative advantage becomes especially important when thinking about trade. In short, nations produce the things they can produce most efficiently. The opportunity cost of production is all of the things that a nation chooses not to produce. If they cannot be as efficiently and profitably produced domestically, then it makes economic sense to trade for them. If an economy produces one good over another because it can produce it more efficiently, then it is making an economic decision based on comparative advantage. The implications of this in our time can be significant, as is often seen with businesses that relocate their manufacturing centers away from the United States and to areas where their goods can be produced more efficiently and profitably.