In a "traditional", symmetric, war, you have two sides and each has approximately the same capabilities, strengths, and weaknesses. Asymmetric warfare refers to the fact that one side has a vastly different set of strengths and weaknesses. Basically, in this particular case, the US has a vast, traditional military. They are going to attack and defend in units of soldiers with tanks, firearms, missiles, etc. The Iraqis are going to attack with bombs, booby-traps (or IEDs, apparently, according to today's parlance), and so on.
Another good example of an asymmetric war occurred about 225 years ago. One side was a very traditional military and the other side fought with a series of irregulars and guerillas. It has become known as the American Revolution.
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Bitt Faulk