The most distinguishing characteristic of the Roman Empire was the presence of an Emperor. The Emperor was a towering figure in the Empire and even the world stage, as Rome extended from modern day England to North Africa to Eastern Europe and Turkey.
Second, the Roman Empire spent a lot of time and energy creating a law code. This was, undoubtedly, one of the greatest achievements. This started in the Republic, but it took huge strides during the Empire. Under Theodosius and Justinian, the Roman law codes became impressive. In fact, Western modern law is heavily indebted to Roman law. First year law students even take a class in Roman law.
Third, another characteristic of the Empire was the presence of many slaves. Arguably, Rome was one of the greatest slave holding people in the history of the world. This is one of the blights of Rome, but it should also be said that some slaves could become very powerful. There is evidence that some people sold themselves into slavery to move up the social ladder.
Finally, towards the end of the Empire, Rome embraced Christianity. This fact helped to establish the Roman Catholic church.