A terrorist group that controls a (now reduced) amount of territory in parts of Iraq and Syria proclaims itself a "caliphate" and an "Islamic state," designations widely rejected by Muslim scholars and the vast majority of practicing Muslims.
Western media sometimes refer to the group as "the Islamic State" (or "IS"), which is what it would like to be called, since it aspires to rule the whole world and not just the small and shrinking piece of territory that it currently controls. More commonly it's called "ISIS," for "the Islamic State and Iraq and Syria," or "ISIL," for "the Islamic State of Iraq and the Levant," the latter closer to an English translation of its original name.
But there's a lot to be said for calling it "Daesh," an Arabic acronym pronounced something between "Dah-esh" and "Dash," that's essentially equivalent to ISIL but has a significant advantage: Daesh itself reportedly hates the name, because in the Arab world its opponents have turned it into a sneer, as explained in the video below.
Of the other options, I personally prefer "ISIL" to "ISIS" because the latter is the name of an Egyptian goddess widely worshipped in the ancient world including the Roman Empire, and she doesn't deserve association with the group.by