Rome is the capital of the country of Italy, easily recognized on a map by being boot-shaped. More than 2000 years ago, even hundreds of years before Jesus came to earth as an infant, the city of Rome began to form. It would be the center of the Roman empire, the next empire you are learning about.
Rome, like other cities of the time period, was controlled by kings, that is until the Romans got control of it. They stopped having rule-by-king and created a republic, where rich men acted as senators, deciding on the laws of the land.
Any free man could become a citizen and have a vote. You could be a citizen by being born in a Roman city or by buying your citizenship. We read about both those ways of becoming a citizen in the Bible when Paul points out to his captor that he is a Roman citizen by birth, whereas the guard had bought his citizenship. Women and slaves could not become citizens or vote.
Rome conquered other territories and soon it was no longer just the city of Rome. It included other cities and areas. The leaders of the conquering army grew more and more powerful. Julius Caesar was the first of the generals who grew so powerful he almost became emperor, ruler over Rome and all the areas Rome had conquered. He was famously murdered to keep him from taking power.
After Julius, a man did become emperor in 27 BC. He was considered a pretty good emperor. His name was Octavian but took on the name Augustus. (Julius/Augustus, July/August – There is a connection!) He is known as Augustus Caesar. Caesar is a title, not a name.