"Skirt steak" has two slightly different definitions: one in American-English, and a slightly different one in British-English. They once referred to precisely the same cut of
beef, but the term's meaning in modern British-English has
morphed.
In the New World, the original definition prevails: a skirt steak is the cut of beef that comes from the very center of the cow's belly, between the brisket in the front, and the flank in the back, (hence, "flank steak"). The center portion, the "plate," is where the animal's diaphragm muscle is located, and this is the source of skirt steak. This definition is reinforced by the The United States Department of Agriculture, which makes it its business to define, among many other things, precisely what a cut of meat is, legally speaking.
Plate-cut skirt steak is commonly used in fajitas and other southwestern-United-States dishes—though certainly not exclusively so—and requires a little trial-and-error to prepare correctly, in my experience.
Alton Brown (and Roninspoon), recommend a fast-and-hot preparation: 30 to 90 seconds on each side, and cut against the grain. Pint recommends flash-frying it with oil and red wine. In any event, skirt steak has a reputation for being tough, but this is probably because inexperienced chefs overcook it. Perphaps because of its reputation, skirt steak is also a rather inexpensive cut of beef (in the United States).
In British-English, "skirt steak" usually refers to the portion of the cow that Americans would call the "flank" (i.e., the distal portion of the underbelly, just adjacent to the hind legs).
In both British- and American- English, skirt steak is a boneless cut of beef.
Both definitions make sense; the word "skirt" generally refers to a hanging periphery, and so, if you think of a cow in "vertical" terms, the periphery of its belly is the center, where it hangs lowest. And then again, if you anthropomorphize it, you could think of the 'lowest' part as being the part most distant from its head.
Sources:
1. http://www.foodreference.com/html/fskirtsteak.html
2. "skirt steak", "diaphragm", and "skirt", in Merriam-Webster Online (www.m-w.com)
3. http://whatscookingamerica.net/Q-A/SkirtSteak.htm
4. http://www.cooks.com/rec/doc/0,1626,146174-224203,00.html