The simple answer to this question is: when one country exerts its will over another country and extends its borders or kingdom.
The very first example of an empire in history (that is widely accepted and known) is the Akkadian Empire. The Akkadian Empire was founded by Sargon sometime in the late 24th century b.c. It was an empire that included both the Akkadian and Sumerian cultures. The Sumerian culture is a very famous one, but this post is not about that. There of course have been many other famous empires throughout history, many of them feature prominently in the Bible. Off the top of my head these empires include: Egypt, Babylon, Assyria, Persia, Alexandrian Greece and Rome.
There is a very common thread all ancient empires hold in common. The king or emperor considered his culture and empire to be the greatest in the world. His intention was very clear- he wanted to take over all nations of the world and subdue them to himself. These emperors even bestowed upon themselves god status, they believed they were descended from the gods, they believed they were gods themselves.
That emperors believed they were gods and that people should worship them is no secret. The pharaohs of Egypt were famous for such behaviour. Nebuchadnezzar, in the time of the Jewish exile to Babylon also carried on such behaviour. He built a big statue of himself and insisted that all people worship the statue.
A god like complex is not the only thing that is problematic or sinful about an empire. The simple fact of exerting one's will over another is obviously sinful. We know this to be true on an individual level. The same is true on a cultural level. For one culture or nation to exert its will over another culture is sinful. To force another culture to take up language and customs is abusive. This has also been a very common thread among the practices of empires.
It would be a worth while topic of research to look into ancient empires and see how they violated God's precepts. There are many examples in the old testament of this. Quite often we know that God considers their practices to be quite evil. He often waits to judge an empire when its "sin has reached its full measure". God's judgement over the Egyptian empire can be seen in the time of the Exodus. God sends clear warning to Nebuchadnezzar as the emperor of Babylon. (Many seem to forget that Nebuchadnezzar actually listened to God in the end).
In following posts I would like to look at how these threads also existed in the Roman empire and how pivotal that was in early Christianity. I would also like to look at how the concept of empire is still very alive in todays world, and still affects nearly everything we do in society including the very practices of church.