Originally an emperor was a ruler who recognised no limitations to his power. Besides proclaiming his word law and claiming a unique connection with the divine an emperor by definition recognised no other ruler as his equal. He was above mere kings and recognised no imperial title but his own. In fact since technically there could only be one emperor under the sun, in as much he did not rule over the whole of creation this was only a consequence of a certain barbarian part of the globe being unworthy of his attention or alternatively a slight against his person and a strictly temporary condition.
Therefore technically an empire is a state which recognises no other realm as its equal and, provided it sees them worth the hassle, seeks to incorporate them all. In practice this definition is too narrow to be useful. In Europe it is only meaningful until the end of antiquity when the emperor, ceasing to have divine properties, progressively became just another title a ruler could claim up to the point when even Simeon I of Bulgaria, a powerful ruler but only in regional terms, could style himself an emperor (tsar).
Another definition of what makes an empire can be looked for in the etymology of the word. In Latin imperium means power, in the sense of possessing coercive authority over someone. This is a tempting definition of imperialism – to rule over anyone but yourself – for a libertarian to adopt, but is too broad to be practical. From a libertarian viewpoint any claim to right to rule over anyone at all is illegitimate no matter what. However if the claim is perceived to be legitimate, most of all by those subject to the rule themselves, then the claim for all practical purposes carries with it the same consequences as if it would indeed be legitimate.
Rather an empire is a state whose claim to power is in some part, no matter how small or large, illegitimate not just philosophically (as every state is) but also illegitimate in practice because it is not lent legitimacy by a critical mass of people. Sometimes this crisis of legitimacy can be present over the whole geographic extent of the empire, but usually it is present only in certain regions.
In the understanding of the present day an empire is a state which rules over peoples of different ethnicity than is that of its ruling class. However this is inaccurate and lazy, akin to defining automobiles as road vehicles with four wheels. A difference in ethnicity between the ruled and the rulers is the number one catalyst for crises of legitimacy, but it is neither the only one nor does it always cause legitimacy of the imperium to be put under question. Besides ethnicity in itself is a subjective category. What to someone is an ethnicity to someone else merely a subgroup within a larger ethnicity or vice versa. Additionally an ethnic group may be thought of as part of one ethnicity by some but a part of other ethnicity by others.
It would likewise be overly simplistic to equate imperialism with expansion. Whether the state is lent legitimacy or not rests upon the populace whose reasoning is in accordance to the norms of its age. Therefore imperialism is that expansionism which defies the accepted norms of its time. An Italian prince who in the middle ages sought to do what Sardinia-Piedmont did in the 19th century and unify all of Italy under his rule, with justification that it is a travesty for a single people like the Italians to be kept separate by arbitrary borders of princely states, would be seen as engaging in what we now call imperialist expansionism. What could justify territorial expansion in the middle ages were titles, but not the doctrine of nationalism. It is what prompted the English kings during their 14th and 15th century adventures in France maintain the pretense of claiming the French crown - to make their invasions which never actually intended to capture the crown of France appear less imperialistic.
Simply that state is an empire which rules over a geographic territory that someone else than itself has a better claim to. What is a better claim is entirely subjective, yet very easy to determine given some intellectual honesty and a rudimentary understanding of the world view of the populace of the geographic territory in question. Does the populace think of their present rulers as legitimate or do they think there is a better candidate whose rule would be more legitimate? If the answer is in the affirmative then the present rulers are imperialists. Also it must be pointed out that legitimacy does not rest on popularity. Legitimacy is not established in the absolute but in relation to an alternative. Thus a deeply unpopular ruler can maintain legitimacy if he is not challenged by pretenders whose potential reign would seem to be more legitimate than his own.
The fact that any state exists is a testament to the fact that a critical mass of people in at least one geographical area that it rules over think of it as a legitimate institution, in the age of colonialism this area would become known as the metropola. What that critical mass may be is impossible to determine precisely. It is by no means something that can be represented by a simple proportion of the populace as a whole. In a medieval kingdom it was enough that the nobles, the clergy and the burgers thought of king as a legitimate ruler. But whether the serfs and slaves without either power or freedom experienced the state as naked violence and force was of little practical consequence. To take an extreme example the practical legitimacy of Sparta did not rest on the attitudes of the powerless Helots but merely on those of the Spartans.
Also because at the heart of the subject of imperialism is legitimacy it means a state which could previously not be considered illegitimate can overnight become illegitimate as the perception of what justifies rule changes among the populace. However it much more often occurs as a new populace in a newly conquered region is added to it. We generally refer to those states as empires which go against the norms of their time in a blatant way. To states whose territorial extent mocks its feeble claims at legitimacy and whose rule rests on nothing but power in numerous regions. However we could just as easily speak of imperialism when talking about small states. For example, Serbia and Greece, not even medium powers, after the Second Balkan War were imperialistic in regard to their hold on Macedonia whose population was neither Serb nor Greek. In this respect we can talk about two mini-empires.
Because a hold of an empire on its illegitimate holdings rests on force only it is inherently unstable. This does not mean that the territory will be constantly up in arms against the centre, for the costs of rising up and not succeeding are great, however it does mean that the populace is not reconciled with the rule from the centre and tolerates it only as something to be suffered temporarily that is, for the time being, and is likely to take advantage of any serious crisis of the centre to try to break free. Now, an empire can sometimes maintain its hold on such an imperial possession until the attitudes as to what makes a legitimate rule slowly shift and it starts to be seen as legitimate by more and more classes until after a number of generations the possession becomes an integral, legitimate part of the empire rather than just a colonial holding. This however rarely happens.
The chances for success can be increased if the empire itself redefines the grounds on which it claims legitimacy to something more acceptable, for example a purely dynastic empire could cease to present itself as such and presents itself as a federation of equal autonomous nations. However this too is rare, presentation in itself is meaningless. Reinventing oneself must be accompanied by actual far reaching reforms or else it is bound to be seen as disingenuous and will not lessen the ire of the subjugated all the while making them more self-confident. In practice imperial possessions are only ever turned into integral regions by migration. By essentially transplanting an integral region into a newly conquered area.