The Cailph or Khalifah was the designated successor to Muhammad, the Prophet and founder of Islam. After the death of Muhammad, Islam split over the issue of who the Cailph would be. Some followed Abu Bakr while other chose to follow Ali, Muhammad’s son-in-law. This great split created the Sunni and Shia branches of Islam. Eventually, the two sides were somewhat reconciled when Ali was elected the 4th Caliph.
The Caliphate spread as Islam spread, and soon all the major cities in the Arab world fell under the sway of the Islamic Caliphate. By the time that the Umayyad Caliphate, which began with the election of Mu'awiyah as the founder of the 6th Caliphate. By then North Africa, Spain, Arabia, Persia and Parts of western Russia were controlled by Muslims.
So the Caliph’s power was extended by both conversion and conquest since all Muslims looked towards him as a political and spiritual leader.