Khalif (pronounced Khaleef) means successor. A Khalif is a leader of the Muslim Ummah (nation/peoples). After Prophet Muhammed (pbuh&hp) died there came after him numerous khalifs (successors) who were called Khalifs (Khaleefs).

The famous first four Khalifs are:

1 - Abu Bakr bin Abu Qahafa (RA)
2 - Umar bin al-Khataab (RA)
3 - Uthman bin Afaan (RA)
4 -Imam Ali ibn Abi Talib (AS), AmirUl-Mo'menin

They are titled Al Khulafa' ar-Rashideen - The Rightly-guided Leaders.

Subsequent leaders were also called Khalifs as they had rulership of the whole Islamic Ummah (nation/peoples). Each khalif was titled 'Ameer al-Mu'mineen' (Commander of the Faithful) even though this title was given to Imam Ali by the Prophet exclusively.

The Khalifate issue is quite controversial as the purpose of leadership was to manage the Muslim Ummah. The Shia Muslims argue and state that the Prophet (SAW) chose Ali ibn Abi Talib (AS) to be the leader after his departure and his sons after him, as an order by Allah.