Original: The early leaders of the Muslim nation following Muhammad's (570 - 632) death were called "Khalifat Rasul Allah", means the political successors to the messenger of God (referring to Muhammad).
Simplified: Some of the early leaders of the Muslim community following Muhammad's (570 - 632) death called themselves "Khalifat Allah", meaning representative of God. But the other title of "Khalifat rasul Allah", meaning the successor to the prophet of God, became the common title.