In the early days of the Roman Republic, the princeps was simply the leading senator, who was elected by the other senators to preside over the Senate and to carry out certain ceremonial functions. Over time, the power and influence of the princeps grew, and he eventually became the de facto ruler of Rome. By the end of the 1st century BC, the princeps had become the emperor, and the term "prince" was used almost exclusively to refer to him.
The emperor was the head of the Roman state, and he held absolute power. He was the commander-in-chief of the army, the chief lawgiver, and the chief judge. He also controlled the finances of the state and the appointment of all government officials. The emperor was considered to be a god on earth, and he was worshipped as such.
The title of "prince" was also used to refer to the heir apparent to the throne. The heir apparent was usually the eldest son of the emperor, but he could also be a younger son or even a nephew. The heir apparent was given the title of princeps iuventutis (prince of the youth), and he was groomed to succeed his father as emperor.
The term "prince" was also used to refer to certain high-ranking military commanders. The principes were the second rank of soldiers in the Roman army, after the triarii. The principes were typically experienced soldiers who were well-trained and well-equipped. They were often used as the main attack force in battle.