The Kurds are an ethnic group spread across a couple of different countries in the Middle East: Iraq, Turkey, Syria, Iran IIRC.. The Kurds have never had their own state and there's been a fairly strong movement at times for the establishment of an independent and unified Kurdistan. This is what has caused the conflict with Turkey. About 17-18% of Turkey is Kurdish, with those numbers mostly concentrated in the eastern part of that country. For the last couple of decades Turkey has been engaged in a conflict with the Kurdistan Workers Party (PKK), a group which Turkey and the US consider terrorists, and who support an independent Kurdish homeland. A couple years ago, Turkey negotiated a cease fire with the PKK, but that has fallen apart in recent weeks.
Turks also faced hostility in other countries. In Iraq they were subjected to attempted genocide by dictator Saddam Hussein, including the use of chemical weapons. This caused the US to establish "no fly zones" in northern Iraq which allowed the Kurds to develop a high level of autonomy. The Kurds in Iraq have generally been very pro-American and the Kurdish region of Iraq has been very peaceful compared to the rest of that country following the US-invasion. The Kurdish Regional Government in Iraq continues to be semi-autonomous but still relies on the Iraqi central government for most of their revenue. The KRG is fairly democratic and less corrupt than most of the other governments in the region. In 2014, when ISIS began pushing towards Kurdish territory in Iraq, and even won some battles, the US intervened with airstrikes. The Kurdish region of Iraq has been flooded with refugees, mostly Arabs and other non-Kurds, fleeing ISIS. The Kurds have their own military force, the Peshmerga ("Those Who Face Death") which is separate from the Iraqi military and has performed pretty well against ISIS in combination with American air strikes. The Kurds are mostly Sunni, like ISIS, but they identify mostly by their ethnic identity and not their sectarian one. They're also much more secular and religiously moderate and generally hate ISIS with a passion. (as you may have figured out from the name, the Turkish Kurdish organization PKK is a Marxist organization).
Kurds also live in Syria, particularly in the Northwest. They've also engaged heavily in the fighting there and have had a lot of success in fighting ISIS. One of the main Syrian Kurdish groups is the People's Protection Units or YPG, which is allied with the PKK. One of the most notable successes of the Kurds in Syria was the defense of Khobani, a Kurdish city in northwestern Syria which ISIS had beseiged for an extended time. Kurdish fighters from several countries poured in and even though the city was largely destroyed by the fighting, ISIS had to retreat. They've also advanced into ISIS controlled territory. At one point IIRC they were within several dozen miles of the ISIS capital.
But the convoluted politics there make things difficult. Despite their pro-US stance and their relative success in fighting ISIS, the US is reluctant to arm the Iraqi Kurds for fear that they will finally break fully with Iraq. The US is supporting YPG efforts against ISIS in Syria, but officially lists their ally the PKK as a terrorist group. The US has just concluded an agreement for Turkey to get more involved in the fight against ISIS, but the Turks have begun attacking the PKK who are also engaged in fighting ISIS.