The Kurds have their own country, but it isn't "internationally recognized", so it doesn't show up on any maps. Militarily and politically, however, the Kurds control a fair-sized geographic slice of Turkey and Iraq.
Interestingly, the Kurds hate both the Turks and the Iraqis.
Moreover, the Kurds want to become internationally recognized. To do so would give them a seat at the UN, the right to various IMF/worldbank aid, the right to sell oil without paying bribes to Turks or Iraqis, and other major perks.
So is it any surprise that the Kurds are welcoming American troops with open arms as well as willing volunteers ready to fight the Iraqis?
Diplomatic recognition for the Kurds by the U.S. and UK would instantly give the Kurds what they have been fighting for over the past century or more. Furthermore, Kurdish fighting might expand the defacto border of the Kurds' territory into some prominent, oil-rich land in what we currently call Northern Iraq.
...And such "recognition" would not be out of the question if the Kurds were to win a single major battle for a city such as Tikrut or Mosul or Kirkut.
In contrast, Turkey followed the UN's path into irrelevancy. Had Turkey played ball with us, they could have secured a promise to not diplomatically recognize the Kurds' country.
However, as things stand today, there is no longer any such guarantee of our future diplomatic behavior.
Thus, Turkey and Iraq now both stand to potentially lose territory (from their official international borders, at least) to the Kurds in this war.
Let's hope that Turkey considers the promises made to them by France (in exchange for complicating the U.S. battle-plan) to be worth this new potential development...