The justification of the state refers to the source of legitimate authority for the state or government. Typically, such a justification explains why the state should exist, and to some degree scopes the role of government - what a legitimate state should or should not be able to do.
There is no single, universally accepted justification of the state. In fact, anarchists believe that there is no justification for the state at all, and that human societies would be better off without it. However, most political ideologies have their own justifications, and thus their own vision of what constitutes a legitimate state. Indeed, a person's opinions regarding the role of government often determine the rest of their political ideology. Thus, discrepancy of opinion in a wide array of political matters is often directly traceable back to a discrepancy of opinion in the justification for the state.
The constitutions of various countries codify views as to the purposes, powers, and forms of their governments, but they tend to do so in rather vague terms, which particular laws, courts, and actions of politicians subsequently flesh out. In general, various countries have translated vague talk about the purposes of their governments into particular state laws, bureaucracies, enforcement actions, etc.
The following are just a few examples.
In feudal Europe, the most widespread justification of the state was the divine right of kings, which stated that monarchs draw their power from God, and the state should only be an apparatus that puts the monarch's will into practice. The legitimacy of the state's lands was derived from the lands being the personal possession of the monarch. The divine right theory, combined with primogeniture, became a theory of hereditary monarchy in the nation states of the early modern period. The Holy Roman Empire was not a state in that sense, and was not a true theocracy.
The political ideas current in China at that time involved the idea of the mandate of heaven. It was similar to the divine right in that it placed the ruler in a divine position, as the link between Heaven and Earth, but it differed from the divine right of kings in that it did not assume that the connection between a dynasty and the state was permanent. Inherent in the concept was that a ruler held the mandate of heaven only as long as he provided good government. If he did not, heaven would withdraw its mandate and whoever restored order would hold the new mandate. This is true theocracy; the power and wisdom to govern is granted by God, not by human political schemes, and can be equally removed by God. This is also the idea presented in the Judeo-Christian Bible from the time Israel requests "a king like the nations" through to Christ himself telling his contemporary leaders that they only had power because God gave it to them. The classic Biblical example is Nebuchadnezzar who created the Babylonian empire because God ordained his power, but who later ate grass like a cow for seven years because he deified himself instead of acknowledging God. Nebuchadnezzar is restored when he again acknowledges God is the true sovereign.