The full form of ISIS is: The Islamic State of Iraq and Syria.
The terrorist organization is known by several other names though:
ISIL: The full form is "Islamic State of Iraq and the Levant" (the Levant is a term that is most often used to describe a part of the middle east which includes Syria, Jordan, Lebanon, Palestine, Israel, Cyprus, Turkey).
In Arabic, the group is often referred to through the abbreviation as 'Daesh' - the full form of which is "al-Dawla al-Islamiya al-Iraq al-Sham", almost the exact translation of the ISIS abbreviation mention above.