Since this month is August, named for the first Roman emperor, Octavian (Augustus), the first term relates to "firstness" and the type of ruler of Rome that began during Octavian's reign.
The term Principate can refer to the period of Roman emperors down to A.D. 476. Sometimes "Principate" is distinguished from the later imperial period known as the Dominate, that began in the late 3rd century with the creation of the Tetrarchy. [See Emperors Timeline.] With the recent spate of books on the later Roman Empire, this distinction may be more common than traditionally. It was during the Dominate that people would prostrate themselves before their lord and master, the emperor, but at least at the beginning of the Principate, the emperor attempted to maintain the illusion that he wasn't so much above the rest of the Roman people as simply first.
The word principate is related to the Latin term princeps civium or princeps civitatis which was used in the Republic to refer to the governmental leaders, the consuls, without offense. It is from princeps that we get our word prince, but princeps did not mean the son of a king or an hereditary monarch, although the men eligible to become consuls were the nobility of Republican Rome. Princeps was not an official title. The Oxford Classical Dictionary says it is the equivalent of the Greek ἡγεμών (hegemon).
Cicero (off.1.26) called Caesar's rule principatus. It's from this Latin word that we get today's term.
Source: The Roman nobility Gelzer, Matthias, 1886-1974. Basil Blackwell, 1969.