For a little background - The Kurds are Sunni Muslims. The Sunnis believe that Muhammad had no rightful heir and that a religious leader should be elected through a vote among the Islamic community's people.
The main goal of the Kurds was to pursue the goal of greater autonomy and even outright independence against the Iraqi nationalist Ba'ath Party regimes, which responded with brutal repression.
The significance of the Kurds is their quest for independence and themselves being the largest people without a state.
I am not an expert, however I hope this helps!