According to the Arabic lexicon, khilāfa (caliphate) literally means taking the position of others in order to perform the legal and religious rights behalf on them. It is also used in the meaning of vicegerency and successor in the Qur'an.
In Islam, the Prophet Muhammad is the Seal of the Prophets and no-one can take the place of the Prophet in his position as Messenger of God. However, other Muslims can represent his position as a ruler, for the Qur'an states, “O you who believe! Obey God and obey the Messenger, and those from among you who are invested with authority.”
The first ruler for Muslims in Islamic history was the Prophet Muhammad. He became the head of state for a cosmopolite society, which consists of Jews, paganist Arabs and Muslims. However, the Prophet did not state who would be head of state after his death, nor did the Qur'an assign anyone for this job. Choosing a ruler for Muslims is a political issue; therefore it is left to people.