At the time Octavian/Augustus established the principate, Rome was exhausted from years of civil wars and disorder. According to Tacitus, most of the generals and potential leaders who could have opposed him had been killed off in those wars. In addition, it was partly through massive bribes to the army and (again in Tacitus's view) the providing of "cheap grain" to the population at large that Augustus pacified the people and prevented any active opposition to his leadership—in which he basically absorbed the roles of the other elements of Roman government into his personal, one-man rule.
It's not an exaggeration to say that not only did Augustus create the Pax Romana but that he laid the foundations of modern Europe during his period in power. The stability of his reign secured the territorial expansion that had occurred under the Republic. He continued the legacy of his great-uncle Julius Caesar, and the role of Rome as a bringer of peace and civilization to other peoples became an explicit element of the Roman consciousness.
It's not an accident that Rome's national epic, the Aeneid, was written during his reign. Virgil expressed the view that the gods had endowed Rome with the purpose of leading the world and that now "the iron gates of war will close." Literature flourished, and even Augustus's empire-wide census can be said to have influenced world civilization—as alluded to in the New Testament at the point where the Christian religion began.
Unfortunately, one cannot say the same for the rest of the Julio-Claudian dynasty. Though modern historians have questioned Tacitus's condemnation of Tiberius, he and the other Caesars who followed Augustus hardly lived up to the standards Augustus set. Tiberius and Claudius, despite their problems, were competent rulers, but Caligula and Nero were irresponsible and borderline psychotic. The fact that the imperial system became chaotic after Nero's suicide, with the Year of the Four Emperors, is an indication that the Julio-Claudian dynasty had not fulfilled the promise both Augustus and his literary admirers had intended or prophesied.