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The word khilafah is a noun of state, or condition, deriving from the third person singular perfect indicative active - khalafa, 'he succeeded', 'was the successor of', 'replaced', 'substituted', 'deputed', 'came after' - of the root kh-l-f, and means 'the state of being a Depute', or 'the concept of having a Depute'. The Depute is known as the khaleefah (the '-ah' ending is an intensifier or energiser for the expression): the plural of the word is khulafa.
The first of these refers to the announcement of the Almighty that He wished to place a Vicegerent on the Earth, and so He created Nabi Adam peace be upon him. The modernisers, or Islamists, (or mustaghriboun or, perhaps, mustafrinjoun), have taken this to mean that all mankind are therefore of that degree.
Although we may all aspire to it (and may have the capacity to attain it) in fact the spiritual actuality of khilaafatu-Llahi fi-l ard is among the highest levels of wilayah, belonging to the Messengers and the Prophets (peace be upon them all) and to the High Saints. A person who has attained that degree is obeyed by all Creation as though he or she were the Almighty Himself: Queen Victoria did not send a Viceroy to India but to be obeyed as though he were she herself.
He says,"And He it is who esteemed you Vicegerents of the Earth and raised some of you above others in degrees so that He might test you in what He has given you;..." (Q, Souratu-l An'am, 6:166). We may each of us become such; but we have not necessarily got there yet,... even though the Islamists may be averse.
The second is currently the chosen buzz-word of a group whose stickers in 1996 could be seen around the UK like so much graffiti. Nevertheless, as a 'society for the promotion of khilafah consciousness' that group has done good work in reviving something that many had wished to consign to oblivion. This is the 'Successor of the Prophet peace be upon him' - the Khaleefatu-r Rasoul, or Caliph - about which office, and the incumbents of it, are many ahadith. From it derive the operational form of most institutions of the Islamic State, and the 'government' or 'authorities' (the Sultan) derive their imperium. In the absence of a zahir Caliph he is deputised by the batin Caliph, namely the Qutb of the Awliya; for without a Caliph, the ummah would be like an orphan, or a body without a head, and the legitimacy of the Shari'ah would suffer, as Christiaan Snouck Hurgronje hoped.
We were enjoined to "obey the Caliph even if he flay the skin off your back" as one hadith states. There is no room for manoeuvre: just because the Caliph was an Ottoman of Turkish origin was no reason at all for Arab treason at the behest of the Triple Entente powers in 1916, no matter how unbearable the provocation from militant Turkish nationalists.
But just because a lieutenant colonel of infantry drove the Incumbent and the imperial family out in 1924 does not mean that the Caliphate was no more, and that the office were abolished just because he said it was. Something that was decreed of the Almighty, and appointed by His Messenger (peace be upon him), cannot be abolished by a man - even a Turkish lieutenant colonel of infantry.
And even if 'the ummah' could 'elect' a Caliph 'by democratic means', it is not necessary. Islam is a universal religion; neither it nor its offices is bound to any one part of the globe. The imperial family still exists. So there has never ceased to be an Incumbent, even if his office has been nominal for the last 75 years. It is up to us now to find out who he is, and to find an office for him to move into...walaw kariha-l kafiroun.
wa-Llahu a'lam bi-s sawab wa mina-Llahi-t tawfeequ wa-l hidayah