The Roman empire was certainly one of the greatest and largest ever. The empire became so large by 285 AD that it became impossible to govern from one location in Rome. It was the emperor Diocletian who who took the bold step to divide the Roman empire into two. The Eastern Empire was governed out of Byzantium, later called Constantinople. It was the Western Empire that was governed otu of Rome.
The two new empires were known as the Roman Empire, but in time, the Eastern Empire began to prefer the Latin language and thus began to lose the character of the traditional Roman empire. Both halves of the Roman Empire continued in its prosperous position until Emperor Theodouius I (395 - 395 AD). At this time, several internal and external forces impacted the breaking up of the two halves as well.
When you asked this question, did you think about the world today? Isn't it interesting that we are still split calling ourselves Western and Eastern, having developed different cultures. In the case of Rome, the split was not due to different ideas or cultures: it was all Roman. But success had been too great. The Roman Empire, by the time of Theodosius, was immense coving most of Europe, North Africa, and parts of Asia.
It made communication and management too difficult. Before he died, in 395 AD Theodosius decided the answer was to split the empire West to East. His successor, Diocletian, carried this out. The Western empire was based in Rome. The Eastern empire, in Byzantium. Two separate emperors would rule their own part but work together against outside enemies. This worked well for the Eastern half of the Empire where spices and other exports brought wealth and stability. It continued for another thousand years after the Westen empire collapsed.
There was a time when the Roman Empire was really large that it was already a bit hard to control. This is probably one of the reasons why it split, it lacked the type of leadership that it used to have. It was not feasible anymore to check and monitor all of the provinces. It was Emperor Diocletian's decision to divide the empire into two halves.
The Eastern Side was governed by Constantinople while the Western Side was governed from Rome. This decision may have made the Roman Empire more vulnerable to the invasion of other groups such as the Barbarians. There are still other reasons why after the division, the Roman Empire fell.
The Roman Empire has been well known in history mainly due to its size. It was enormous. It would take a very long time to get from one side of the empire to the other side. The leader of the Roman Empire at the time that it was the biggest had trouble ruling such a large empire.
Diocletian was an emperor during one part of the Roman Empire. He realized the problem of ruling such a large empire and decided to do something about it. He split the empire into two parts. The western empire included Rome and the eastern empire included Byzantium. The western empire had its own leader and the same for the eastern empire. The western empire ended quickly.