Boko Haram has declared North Eastern Nigeria an Islamic Caliphate. ISIS has declared a Caliphate over Northern Syria and Iraq. So what is a Caliphate?
A Caliph is "the commander of the believers." A Caliphate is an Islamic state led by a supreme religious and political leader known as a Caliph. The Caliph is believed to be a successor to Muhammad. The Caliphate is a unitary state composed of all faithful Muslims (the Ummah), ruled by a Caliph under Islamic (Shari'a) law.
Elected or Appointed
The Sunnibranch of Islam stipulates that the Caliph should be elected by Muslims, or their representatives. However the Shiite Muslims believe that the Caliph should be an Imam chosen by Allah, and not answerable to any electoral base.