Khalaafah to put it simply is rule of law based concept wherein constitution=the quran is supreme not personalities. All institutions and people are given rights and responsibilities within which they are supposed to function as a society or community, each person and institution fulfilling its constitutional obligations to best of their abilities.
They are supposed to be elected for administration by general consensus according to set out quranic criterion as well as quranic set procedures. Only those people who are confident within themselves that they can serve the community are to put themselves forward and they are to be elected only if the community finds them trustable and capable of delivering the set out program that ummah needs to implement in order to achieve the set out goals.
The quran paints a very different picture of islamic ruling system than we are used to. This is why it is going to take some time before khilaafah actually comes about because educating the ummah about the quranic way of government is not going to be easy. Especially under current environment wherein people are not willing to think things through objectively.