Traditionally the Kurds were nomadic herdsmen, but are now seminomadic or sedentary. The majority of Kurds are Sunni Muslims. The ancient Kurdish community near Kabul, Afghanistan left the country during the Afghan Civil War in the late 1970s. For over a century, many Kurds have been campaigning for the right to their own state, which they would call Kurdistan -- by some accounts the Kurds are the world's largest ethnic group without their own state. However, despite promises of the creation of such a state made in the early 20th century, all the region's governments are opposed to it.
They are ethnic group with no country to call home. The turks gave them pieces of land here and there. They refused an autonomus country in North Iraq and they wanted Mosul and the Large cities. They were crushed after that in Iraq.
Basically, Kurdish want to have pieces from Iran, Iraq, Syria, Turkey, and even fro old sovient union to call Kurdistan.