Step-by-step explanation:
The Roman Empire which origins can be argued to either the ascent of Julius Caesar to Dictator, or the acceptance of Octavian Caesar as Augustus (First Citizen). Basically, sometime in the 2nd have of the 1st century B.C.E. At that time, the Roman state or Senatus and Populesque Romanus: Senate and People of Rome or SPQR) held an extreme number of treaties with it's neighbors. Few of the people were considered part of the Republic and only Roman Citizens could vote or hold offices such as Senator, Quaestor, Tribune, or Consul. Most civilizations governed themselves and had a Roman Governor. These "Allies" would also supply soldiers for Auxiliaries to the Roman Legions. At some point in the transition from Roman Republic to Roman Empire an incorporation began of citizenship. This would allow previously non-citizens of the allied civilizations to be granted rights under Roman Law. The concept had never been incorporated by any other civilization. It had always previously been stipulated that family descent would delineate citizenship. This was the first and foremost strength of the Roman Empire the ability to amalgamate it's people into a citizenship. One of the best ways it was able to unify the other populations was the use of it's Language. Because one had to understand Latin to understand it's Laws it became necessary for the people of the Empire to speak the same language and therefore Latin spread to every corner of the empire and displaced many languages in other territories, (this is why there are the Romance Languages, Spanish, Italian, French, and Romanian, all were parts of the Roman Empire for extreme periods of time). The next aspect and probably the most distinguished is the Roman Army. It was the greatest military force of professional soldiers in the Ancient World. It's equipment was standardized as was the training. The soldiers were however more than just well trained and well armed. They were laborers and engineers. Under Julius Caesar they were able to build a bridge across the Rhine in less than two weeks, without machines. They would construct Roads, Aqueducts, Forts, Towns, Bridges, Temples, Walls, and whatever else they needed. This Army/Labor force was mobile and terrifying, drawing on the experiences and fame of Julius Caesar and his memoirs about the Gallic Wars. He and future Emperors would annihilate whole populations of rebellious civilizations (Gauls & Dacians come to mind, also don't forget about the expulsion of the Jews from Judea). All of these factors allowed Roman Law to reign supreme and the peace or "Pax Romana" that occurred for several centuries allowed trade to flourish making Rome the center of the civilized world the envy of the Barbarians.
When you take into account all of theses aspects 1.) Granting of Citizenship 2.) Language 3.) Military force 4.) Construction of military yet civilian necessities 5.) Flourishing trade coupled with extended periods of peace, it becomes easy to understand how one Civilization could be denoted as the Greatest of the Ancient world. To contrast that, after the fall of Rome, Europe entered into a Dark Age that would last nearly 1200 years.
Also unlike what the genius Phil said, there are many civilizations and Nations that lasted after 455 that attempted to use Rome as it's title and claim legitimacy to the Roman Empire, (Holy Roman Empire, Even the Germans use of Kaiser which is a translation of Caesar, the Russian use of Czar is a translation from Caesar and is suppose to represent the inheritance of the Byzantine Empire which was the remnants of the Eastern Roman Empire, lastly it can be argued the the Pope is the present ruler of the Roman Empire through the spirit of Catholicism).