The main difference between the Roman Republic and the Roman Empire concerned the institutions of government. Under the Republic, power was dispersed between the Roman aristocracy and the common people, or plebs. The Senate was the main instrument of power of Roman nobles, whereas the plebs could vote for a tribune to represent their interests. Furthermore, there was no one ruler of Rome; power was shared between two consuls, and both of them were elected to serve one year in office.
In practice, however, the Roman Republic was beset by bitter struggles between powerful aristocrats such as Julius Caesar and Pompey, and it was these struggles that eventually led to the downfall of the Republic and its replacement with the imperial system of government.
Once Octavian—later Augustus—became the first emperor, supreme power was vested in just one man. Octavian was clever in that he didn't openly declare himself as Emperor; the title was conferred upon him by a grateful Senate. He knew what had happened to his uncle, Julius Caesar, when he overreached himself and accrued too much power.
So, at the outset of his lengthy reign, Augustus modestly stated that he would exercise power in accordance with the old traditions. But this was all just for show. In reality, Augustus would come to acquire much more power than Julius Caesar could have dreamed of.
In addition to benefitting from his remarkable ability to hide his true motives, Augustus benefitted from the Roman people's war fatigue. They were fed up of constant strife and wanted peace and stability. And for this, they were prepared to invest Augustus with enormous, almost dictatorial powers.