The word Khalifah refers to the successor or representative of Prophet Muhammad (saas) or to one of his successors. This person acts as the head of state for the Muslim Ummah. Another title for the Khalifah (English Caliph) is Amir Al-Mu'mineen which means 'the leaders of the believers'.
The immediate Caliphs were Abu Bakr As-Siddiq, Omar Ibn Al-Khattab, Othman Ibn 'Affan, and 'Ali Ibn Abi Talib. These were given the nickname of Al-Khulafa'Ar-Rashidun (The Guided Caliphs).
Another use for this word is used for humanity in general. The human being is considered the Khalifah (representative) of Allah on earth according to Allah.